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Surface treatment of perovskite materials with their layered counterparts has become an ubiquitous strategy for maximizing device performance. While layered materials confer great benefits to the longevity and long‐term efficiency of the resulting device stack via passivation of defects and surface traps, numerous reports have previously demonstrated that these materials evolve under exposure to light and humidity, suggesting that they are not fully stable. Therefore, it is crucial to study the behavior of these materials in isolation and in conditions mimicking a device stack. Here, it is shown that perovskite capping layers templated by a range of cations on top of methylammonium lead iodide devolve in conditions commonly found during perovskite fabrication, such as exposure to light, solvent, and moisture. Photophysical, structural, and morphological studies are used to show that the degradation of these layered perovskites occurs via a self‐limiting, pinhole‐mediated mechanism. This results in the loss of whole perovskite sheets, from a few monolayers to tens of nanometers of material, until the system stabilizes again as demonstrated for exfoliated flakes of PEA2PbI4. This means that initially targeted structures may have devolved, with clear optimization implications for device fabrication.

We present new, exact, rotating and accelerating solutions within the framework of five-dimensional Einstein-Gauss-Bonnet theory at the Chern-Simons point. The rotating solutions describe black holes characterized by a single rotation parameter, a mass parameter, and two extra integration constants that can be interpreted as hairs of a gravitational nature. It is noteworthy that the rotation cannot be removed by a large diffeomorphism. We also extend our procedure to dimension seven, providing a new rotating solution with two rotation parameters pertaining to cubic Lovelock theory with a unique vacuum.

This document elaborates on a newly introduced analytical method known as the “Variable Coefficient Generalized Abel Equation Method,” as proposed by Hashemi in Hashemi (2024), designed specifically for addressing the two-mode Cahn–Allen equation. Diverging from conventional techniques that heavily rely on constant coefficient ordinary differential equations and auxiliary ordinary differential equations, our method innovatively incorporates variable coefficient ordinary differential equations within a sub-equation framework. Demonstrating its versatility, we apply this innovative technique to the two-mode Cahn–Allen equation, showcasing its effectiveness and efficiency through the derivation of analytical solutions. Notably, this method emerges as a promising tool for tackling complex nonlinear partial differential equations prevalent in fluid dynamics and wave propagation scenarios. Beyond merely expanding the repertoire of available analytical tools, our approach contributes to advancing solutions for various models within the realm of mathematical physics. Various forms of exact solutions, including exponential-type solutions, Kink solitons, dark solitons, and bright soliton solutions, are obtained for the model under consideration. Moreover, we delve into the analysis of bifurcation, chaotic behavior, and sensitivity within the context of the two-mode Cahn–Allen model, further enhancing the depth and breadth of our study. Three equilibria are analyzed across various classifications, including center point, focus point, saddle point, and node point. Chaotic behavior of the corresponding dynamical system is considered by adding the function ω1sin(ω2ζ). Lastly, sensitivity analysis of the system is conducted by examining different parameters of the model and imposing noise to the initial conditions.

This research investigates the seismic behavior of rigid and flexible cylindrical steel tanks, focusing on tanks with an open top and fully anchored at the base. The primary objective is to evaluate the hydrodynamic pressures exerted by the fluid on the tank walls during seismic excitation. Three widely recognized design approaches—New Zealand NZSEE recommendations, European code UNI EN 1998-4:2006 (CEN, 2006), and American Water Works Association AWWA D100-05 standard (ANSI/AWWA, 2005)—were implemented and compared with high-definition finite element models and then validated against the experimental results. Nonlinear fluid–structure interaction (FSI) was modeled using an Arbitrary Lagrangian–Eulerian (ALE) formulation with the Navier–Stokes equations governing the fluid motion and material and geometric nonlinearities considered in the tank walls. Parametric analyses were conducted to investigate the impact of tank geometry, specifically height-to-radius and radius-to-thickness ratios, on seismic response, identifying a transition between rigid and flexible behavior. The study also examined the influence of seismic input using a set of ten displacement spectrum-compatible ground motions. The findings contribute to a better understanding of the seismic resilience of cylindrical steel tanks, offering valuable insights for improving design standards and safety in earthquake-prone regions where these systems may abound.

Mechanical antennas with rotating permanent magnets are a relatively new type of transmitting antenna in low- and ultralow-frequency (LF/ULF) ranges. The perspectives of the applications are encouraging, especially in the field of non-destructive defectoscopy and communications through conductive media (underwater communications), which is reflected in the articles published in the last decade. This article describes the experimental setup, results, harmonic analysis, and simulation validation for two configurations of mechanical antennas with rotating NdFeB permanent magnets. The emphasis is placed on the known analytical equations, specifically on the matching of the measurement results with the analytical data as well as with the results given by the numerical analysis. Also, several means of measurement are used to validate the results through replicate testing. Through analytical analysis and the performed measurement, this article establishes the basics for designing mechanical antennas with rotating permanent magnets for the considered configurations based on a single static magnetic field measurement. Finally, we explore prospects for future research in this domain as well as the advantages and disadvantages compared to other types of LF/ULF antennas.

Open-pit mining generates significant amounts of waste material, leading to the formation of large waste dumps that pose environmental risks such as land degradation and potential slope failures. The paper presents a stability analysis of waste dump slopes in open-pit mining, focusing on the Motru coalfield in Romania. To assess the stability of these dumps, the study employs the Shear Strength Reduction Method (SSRM) implemented in the COMSOL Multiphysics version 6 software, considering both associative and non-associative plasticity models. (1) Various slope angles were analyzed, and the Factor of Safety (FoS) was calculated, showing that the FoS decreases as the slope angle increases. (2) The study also demonstrates that the use of non-associative plasticity leads to lower FoS values compared to associative plasticity. (3) The results are visualized through 2D and 3D models, highlighting failure surfaces and displacement patterns, which offer insight into the rock mass behavior prior to failure. (4) The research also emphasizes the effectiveness of numerical modeling in geotechnical assessments of stability. (5) The results suggest that a non-associative flow rule should be adopted for slope stability analysis. (7) Quantitative results are obtained, with small variations compared to those obtained by LEM. (6) Dilatation angle, soil moduli, or domain changes cause differences of just a few percent and are not critical for the use of the SSRM in engineering.

The interplay of dynamical correlations and electronic ordering is pivotal in shaping phase diagrams of correlated quantum materials. In magic-angle twisted bilayer graphene, transport, thermodynamic, and spectroscopic experiments pinpoint a competition between distinct low-energy states with and without electronic order, as well as between localized and delocalized charge carriers. In this study, we utilize dynamical mean-field theory on the topological heavy fermion model of twisted bilayer graphene to investigate the emergence of electronic correlations and long-range order in the absence of strain. We contrast moment formation, Kondo screening, and ordering on a temperature basis and explain the nature of emergent correlated states based on three central phenomena: (i) the formation of local spin and valley isospin moments around 100 K, (ii) the ordering of the local isospin moments around 10 K preempting Kondo screening, and (iii) a cascadic redistribution of charge between localized and delocalized electronic states upon doping. At integer fillings, we find that low-energy spectral weight is depleted in the symmetric phase, while we find insulating states with gaps enhanced by exchange coupling in the zero-strain ordered phases. Doping away from integer filling results in distinct metallic states: a “bad metal” above the ordering temperature, where scattering off the disordered local moments suppresses electronic coherence, and a “good metal” in the ordered states with coherence of quasiparticles facilitated by isospin order. This finding reveals coherence from order as the microscopic mechanism behind the Pomeranchuk effect observed experimentally by Rozen et al. [Nature (London) 592, 214 (2021)NATUAS0028-083610.1038/s41586-021-03319-3] and by Saito et al. [Nature (London) 592, 220 (2021)NATUAS0028-083610.1038/s41586-021-03409-2]. Upon doping, there is a periodic charge reshuffling between localized and delocalized electronic orbitals leading to cascades of doping-induced Lifshitz transitions, local spectral weight redistributions, and periodic variations of the electronic compressibility ranging from nearly incompressible to negative. Our findings highlight the essential role of charge transfer, hybridization, and ordering in shaping the electronic excitations and thermodynamic properties in twisted bilayer graphene and provide a unified understanding of the most puzzling aspects of scanning tunneling spectroscopy, transport, and compressibility experiments.

A pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established. The concept of maximal solution for obtaining a unique uncertain solution is introduced. The solutions of uncertain discrete relaxation equations for the integer and the fractional order are obtained. Various numerical examples are accompanied to clarify the theoretical results and study of uncertain system behavior.

Closed-form expressions for the dimensionless velocity, shear stresses, and the flow vorticity fields corresponding to the isothermal unsteady Poiseuille flows of a fractional incompressible viscous fluid over an infinite flat plate are established. The fluid motion induced by a pressure gradient in the flow direction is also influenced by the flat plate that oscillates in its plane. The vorticity field is dependent on two spatial coordinate and time, and it is an arbitrary trigonometric polynomial in the horizontal coordinate. The exact solutions, obtained by generalized separation of variables and Laplace transform technique, are presented in terms of the Wright function and complementary error function of Gauss. Their advantage consists in the fact that the values of the fractional parameter can be chosen so that the predicted material properties by them to be in agreement with the corresponding experimental results. In addition, they describe motions for which the nontrivial shear stresses are influenced by history of the shear rates. It is found that the flow vorticity is stronger near the plate, but it could be attenuated in the case of fractional model.

High-Entropy Alloys (HEAs) represent a transformative class of materials characterized by multiple principal elements and high configurational entropy. This review article provides an in-depth examination of their structural particularities, prediction methodologies, and synthesis techniques. HEAs exhibit unique structural stability due to high-entropy effects, severe lattice distortions, and slow diffusion processes. Predictive models, including thermodynamic and kinetic approaches, are essential for understanding phase stability. Various synthesis methods impact HEA properties, and advanced characterization techniques are crucial for their study. The article highlights current applications and future research directions, emphasizing the potential of HEAs in diverse technological fields.

Considering the widespread presence of switching devices on the power grid (including renewable energy system inverters), network distortion is more prominent. To maximize network efficiency, our goal is to minimize these distortions. Measuring the voltage and current total harmonic distortion (THD) using power meters and other specific equipment, and assessing power factor and peak currents, represents a crucial step in creating an efficient and stable smart grid. In this paper, we propose a power meter capable for measuring both standard electrical parameters and power quality parameters such as the voltage and current total harmonic distortion factors. The resulting device is compact and DIN-rail-mountable, occupying only three modules in an electrical cabinet. It integrates both wired and wireless communication interfaces and multiple communication protocols, such as Modbus RTU/TCP and MQTT. A microSD card can be used to store the device configuration parameters and to record the measured values in case of network fault events, the device’s continuous operation being ensured by the integrated backup battery in this situations. The device was calibrated and tested against three industrial power meters: Siemens SENTRON PAC4200, Janitza UMG-96RM, and Phoenix Contact EEM-MA400, obtaining an overall average measurement error of only 1.22%.

We face significant environmental pollution problems due to various industries, such as the aluminum industry, which generates large amounts of red mud (RM) waste, or agriculture, in which case the use of pesticides creates huge water pollution problems. In this context, the present study offers a better perspective to originally solve both environmental issues. Thus, the main target of the study referred to using RM waste as a filler for preparing composite copolymer beads. Thereafter, this can achieve significant removal of water pollutants due to their adsorption/oxidation characteristics. As evidenced by the changes in chemical structure and composition, thermal stability, morphology, and porosity, RM was homogenously incorporated in poly(acrylonitrile-co-acrylic acid) beads prepared by wet phase inversion. The final assessment for the removal of pesticides by adsorption and oxidation processes was proven successful. In this regard, 2,4-dichlorophenoxyacetic acid was chosen as a model pollutant, for which an adsorption capacity of 16.08 mg/g composite beads was achieved.

This study delves deep into the complexities of the modified nonlinear Schrödinger equation. Through the Galilean transformation, we derive a dynamic system linked to the equation. Using planar dynamical systems theory, we investigate bifurcation phenomena and introduce perturbations to reveal chaotic behaviors. Phase portraits offer visual insights, while sensitivity analysis using the Runge–Kutta method emphasizes solution stability against initial condition variations. Leveraging the planar dynamical system method, we generate diverse solitons, including periodic, bright, and dark solitons. This work enhances our grasp of intricate dynamics and their broader implications.

It is a well-known fact that functional effects like relaxation and retardation of materials, and heat transfer phenomena occur in a wide range of industrial and engineering problems. In this context, a mathematical model is developed in the view of Caputo fractional derivative for Oldroyd-B nano-fluid. Nano-sized particles of copper (Cu) are used to prepare nano-fluid taking water as the base fluid. The coupled non-linear governing equations of the problem are transformed into dimensionless form. Finite difference scheme is developed and applied successfully to get the numerical solutions of deliberated problem. Influence of different physical parameters on fluid velocity profile and temperature profile are analyzed briefly. It is observed that for increasing values of fractional parameter (α), fluid velocity increased, but opposite behavior was noticed for temperature profile. Nusselt number (Nu) decayed for advancement in values of heat source/sink parameter (Q0), radiation parameter (Nr), volume fraction parameter of nano-fluid (ϕ), and viscous dissipation parameter (Ec). Skin friction (Cf) boosts for the increase in the values of magnetic field parameter (Ha). It can also be noticed that the extended finite difference scheme is an efficient tool and gives the accurate results of discussed problem. It can be extended for more numerous type heat transfer problems arising in physical nature with complex geometry.

Treponema pallidum, a spiral-shaped bacterium, is responsible for the sexually transmitted disease syphilis. Millions of people in less developed countries are getting the disease despite the accessibility of effective preventative methods like condom use and effective and affordable treatment choices. The disease can be fatal if the patient does not have access to adequate treatment. Prevalence has hovered between endemic levels in industrialized countries for decades and is currently rising. Using the Mittag-Leffler kernel, we develop a fractal-fractional model for the syphilis disease. Qualitative as well as quantitative analysis of the fractional order system are performed. Also, fixed point theory and the Lipschitz condition are used to fulfill the criteria for the existence and uniqueness of the exact solution. We illustrate the system’s Ulam–Hyers stability for disease-free and endemic equilibrium. The analytical solution is supported by numerical simulations that show how the dynamics of the spread of syphilis within the population are influenced by fractional-order derivatives. The outcomes show that the suggested methods are effective in delivering better results. Overall, this research helps to develop more precise and comprehensive approaches to understanding and regulating syphilis disease transmission and progression.

This study analyzed a modified conservative 4D chaotic system is investigated using both integer and non-integer order derivatives. Several dynamical aspects of the said model are explored, such as stable equilibrium points, Lyapunov spectra (LS), attractor projection, Poincare, bifurcations and phase portrait. The system is also analyzed using a singular fractional operator, and the theory of the existence of solutions is established through functional analysis. To obtain numerical results of the fractional order system, a numerical method based on Newton polynomial is applied. The study reveals the presence of hidden and fixed point chaotic attractors for certain fractional order values.

The major objective of this effort is to use the collocation technique (CT) to examine fractional chemical kinetics(CK) and other problem that correlates the condensations of carbon dioxide (CO2) and phenyl glycidyl ether (PGE) with two varieties of Dirichlet and a mixed set of Neumann boundary and Dirichlet-type constraints respectively. The suggested approach depends on the shifted Jacobi collocation techniques along with the shifted Jacobi operational matrix for fractional derivatives of any order, defined in the Caputo sense. Examining a global approximation for temporal and spatial discretizations is the main benefit of the suggested methodology. Additionally, the mathematical method simplifies the fractional differential equations by reducing them to a straightforward problem that just needs the solution of a set of algebraic equations. The arithmetical results and figures show that the suggested approach is an effective algorithm with excellent accuracy for resolving arbitrary order differential equations. A few theorems regarding error analysis are presented and explained. We also compare the numerical results produced using the suggested technique with those results obtained through the existing techniques.

Wireless sensor networks (WSNs) have gained much interest due to their enormous potential in civil and military applications. The power and radio communication capabilities of the sensor nodes are limited. Because sensor nodes have limited resources, they have weak defense capabilities and are attractive targets for software attacks. Worm-based cyberattacks are among the most significant threats to computers and WSNs’ security and integrity. In this article, a five-compartmental WSN epidemic model is considered. We conducted an investigation into equilibrium analysis and the reproductive number, followed by the development of a nonstandard finite difference numerical scheme for our model. The outcomes of our numerical simulations are then presented. This method yields reliable predictions, which can be valuable for regulators when making decisions related to designing and implementing control strategies. Furthermore, some interesting properties of the developed scheme are investigated, such as positivity, convergence, and consistency. The developed scheme preserves the essential characteristics of disease epidemic models like positivity, convergence, and consistency.

We investigate a generalized scale-invariant analogue of the Korteweg–de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation. To conduct a comprehensive analysis, we employ the Generalized Kudryashov Technique (KT), Modified KT, and the sine–cosine method. Through the application of these advanced methods, a diverse range of traveling wave solutions is derived, encompassing both bounded and singular types. Among these solutions are dark and bell-shaped waves, as well as periodic waves. Significantly, our investigation reveals novel solutions that have not been previously documented in existing literature. These findings present novel contributions to the field and offer potential applications in various physical phenomena, enhancing our understanding of nonlinear wave equations.

Bovine Brucellosis, a zoonotic disease, can infect cattle in tropical and subtropical areas. It remains a critical issue for both human and animal health in many parts of the world, especially those where livestock is an important source of food and income. An efficient method for monitoring the illness’s increasing prevalence and developing low-cost prevention strategies for both its effects and recurrence is brucellosis disease modeling. We create a fractional-order model of Bovine Brucellosis using a discrete modified Atangana–Baleanu fractional difference operator of the Liouville–Caputo type. An analysis of the suggested system’s well-posedness and a qualitative investigation are both conducted. The examination of the Volterra-type Lyapunov function for global stability is supported by the first and derivative tests. The Lipschitz condition is also used for the model in order to meet the criterion of the uniqueness of the exact solution. We created an endemic and disease-free equilibrium. Solutions are built in the discrete generalized form of the Mittag-Leffler kernel in order to analyze the effect of the fractional operator with numerical simulations and emphasize the effects of the sickness due to the many factors involved. The capacity of the suggested model to forecast an infectious disease like brucellosis can help researchers and decision-makers take preventive actions.

Zika virus infection is a vastly transmitted disease among humans. It was carried worldwide by international travelers. In 2016, Zika virus infection was present in more than 20 countries and territories in America. Thousands of cases were diagnosed in Cabo Verde, western Africa. Fifty-seven regions suffered from Zika virus in 2020, and the World Health Organization reported more than one hundred thousand cases worldwide. In this work, the modeling and transmission dynamics of Zika virus are studied dynamically and numerically. Positivity, boundedness, reproduction number, equilibria, and local stability are part of the numerical analysis. New nonstandard numerical techniques are examined for the said model. The primary purpose is to maintain the continuous model’s behavior and dynamical properties. The proposed nonstandard finite approximation is studied according to the consistency and local stability of the solutions. Some numerical examples clearly show the improvement of the new schemes compared to other well-known methods.

In the cement concrete manufacturing industry, mixers are critical pieces of equipment that play an essential role. Mixers ensure, by mechanically mixing the materials that make up the concrete, the homogeneity of the mixture. Since the active elements of the mixer in the concrete industry—the mixing blades—come into permanent contact with the mineral aggregates in the mixture formed by water and cement, they are permanently subjected to a strong abrasive–erosive wear process. The authors of this article were concerned with the establishment of tribological models for studying the wear of mixing blades, in order to identify the influence of their constructive parameters on the wear intensity. A complex model (Kraghelsky–Nepomnyashchi model) was adopted for the study. The modeling results revealed that the wear intensity decreases with an increasing blade angle of attack and increases linearly with increasing speed, as well as with an increasing friction coefficient. The modeling results confirm that the wear intensity is lowest when the mixing blade is inclined at a 60° angle, while the highest value is recorded for 30°. By identifying the angle at which the greatest wear of blades occurs, interventions can be made in the design of a more durable mixer (with the optimal installation angle of the mixer blades), thus requiring fewer corrective maintenance interventions. Based on these findings, we conclude that the complex model used in the experiment can provide a convenient and efficient tool for the study of erosive–abrasive phenomena.

Electrical contacts are important circuit components with diverse industrial applications, and their failure can lead to multiple unwanted effects. Hence, the behavior of electrical contacts is a widely studied topic in the scientific literature based on various approaches, tools, and techniques. The present study proposes a new approach to numerical modeling and simulation based on the Holm contact theory, aiming to study the dependence between the electric potential and the temperature within an electrical contact. Structured in five sections, the research was conducted using COMSOL Multiphysics software (version 5.3) and its solid-state mechanics, electric current, and heat transfer modules in order to highlight contact behavior from mechanical, electrical and thermal points of view: the von Mises stress, contact force, electric field amplitude, variation of the electrical potential along the current path, temperature gradient, and dependence of temperature along the contact elements edges were obtained by simulation, and are graphically represented. The results show that the temperature increase follows a parabolic curve, and that for values higher than 4 mV of voltage drop, the temperature of the contact increases to 79.25 degrees (and up to 123.81 degrees for 5 mV) over the ambient temperature, thus the integrity of insulation can be compromised. These values are close (10–12%) to the analytically calculated ones, and also in line with research assessed in the literature review.

Resveratrol (RSV), a naturally occurring phytoalexin, is the most important stilbenoid synthesized by plants as a defense mechanism in response to microbial aggression, toxins, or ultraviolet radiation. RSV came to the attention of researchers both as a potential chemopreventive agent and a possible explanation for the low incidence of cardiovascular disease (CVD) in French people with a high-fat diet. RSV is mainly administered as a food supplement, and its properties are evaluated in vitro or in vivo on various experimental models. RSV modulates signaling pathways that limit the spread of tumor cells, protects nerve cells from damage, is useful in the prevention of diabetes, and generally acts as an anti-aging natural compound. It was highlighted that RSV could ameliorate the consequences of an unhealthy lifestyle caused by an exaggerated caloric intake. This paper reviews the evidence supporting the beneficial effect of RSV for various pathological conditions, e.g., neoplastic diseases, neurodegeneration, metabolic syndrome, diabetes, obesity, CVDs, immune diseases, bacterial, viral, and fungal infections. The study also focused on the chromatographic analysis of trans-RSV (tRSV) in Romanian wine samples, providing a comprehensive overview of tRSV content across different types of wine.

Several numerical techniques for solving initial value problems arise in physical and natural sciences. In many cases, these problems require numerical treatment to achieve the required solution. However, in today’s modern era, numerical algorithms must be cost-effective with suitable convergence and stability features. At least the fifth-order convergent two-step optimized hybrid block method recently proposed in the literature is formulated in this research work with its variable stepsize approach for numerically solving first- and higher-order initial-value problems in ordinary differential equations. It has been constructed using a continuous approximation achieved through interpolation and collocation techniques at two intra-step points chosen by optimizing the local truncation errors of the main formulae. The theoretical analysis, including order stars for the relative stability, is considered. Both fixed and variable stepsize approaches are presented to observe the superiority of the latter approach. When tested on challenging differential systems, the method gives better accuracy, as revealed by the efficiency plots and the error distribution tables, including the machine time measured in seconds.

In this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo–Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.

Artificial intelligence plays a very prominent role in many fields, and of late, this term has been gaining much more popularity due to recent advances in machine learning. Machine learning is a sphere of artificial intelligence where machines are responsible for doing daily chores and are believed to be more intelligent than humans. Furthermore, artificial intelligence is significant in behavioral, social, physical, and biological engineering, biomathematical sciences, and many more disciplines. Fractional-order modeling of a real-world problem is a powerful tool for understanding the dynamics of the problem. In this study, an investigation into a fractional-order epidemic model of the novel coronavirus (COVID-19) is presented using intelligent computing through Bayesian-regularization backpropagation networks (BRBFNs). The designed BRBFNs are exploited to predict the transmission dynamics of COVID-19 disease by taking the dataset from a fractional numerical method based on the Grünwald–Letnikov backward finite difference. The datasets for the fractional-order mathematical model of COVID-19 for Wuhan and Karachi metropolitan cities are trained with BRBFNs for biased and unbiased input and target values. The proposed technique (BRBFNs) is implemented to estimate the integer and fractional-order COVID-19 spread dynamics. Its reliability, effectiveness, and validation are verified through consistently achieved accuracy metrics that depend on error histograms, regression studies, and mean squared error.

This work investigates the computational study of a six-compartmental mathematical model of tuberculosis disease dynamics with the impact of vaccination. Traditional mathematical models presume that all variables are precise and can be measured or calculated precisely. However, in many real-world scenarios, variables may need to be more accurate or easier to quantify, resulting in model uncertainty. Considering this, fuzziness is introduced into the model by taking the contact, recovery, and death rates due to disease as fuzzy membership functions. Two numerical computational schemes, forward Euler and nonstandard finite difference (NSFD), are designed to solve the model. The positivity and convergence for the developed method are investigated, which are significant characteristics of these dynamical models, and it is revealed that these features are preserved in the extended scheme. Numerical computations are performed to support the analytical results. The numerical and computational results indicate that the proposed NSFD method adequately represents the dynamics of the disease despite the uncertainty and heterogeneity. Moreover, the obtained method generates plausible predictions that regulators can use to design and develop control strategies to support decision-making.

The current study presents the numerical solutions of the Wolbachia invasive model (WIM) using the neural network Levenberg-Marquardt (NN-LM) backpropagation technique. The dynamics of the Wolbachia model is categorized into four classes, namely Wolbachia-uninfected aquatic mosquitoes (An∗), Wolbachia-uninfected adult female mosquitoes (Fn∗), Wolbachia-infected aquatic mosquitoes (Aw∗), and Wolbachia-infected adult female mosquitoes (Fw∗). A reference dataset for the proposed NN-LM technique is created by solving the Wolbachia model using the Runge-Kutta (RK) numerical method. The reference dataset is used for validation, training, and testing of the proposed NN-LM technique for three different cases. The obtained numerical results from the proposed neural network technique are compared with the results obtained from the RK method for accuracy, correctness, and efficiency of the designed methodology. The validation of the proposed solution methodology is checked through the mean square error (MSE), error histograms, error plots, regression plots, and fitness plots.

In recent decades, the mathematical modeling of infectious diseases, real-world problems, non-linear dynamical complex systems, etc., has increased significantly. According to World Health Organization, tobacco use is the cause of about 22% of cancer deaths. Another 10% are due to obesity, poor diet, lack of physical activity, and excessive drinking of alcohol. Approximately 5%–10% of cancers are due to inherited genetic defects. The objective is to investigate the impact of time delays in implementing control measures on the epidemic dynamics. The classification of cell population has four compartments: susceptible cells (x), cancer-infected cells (y), virus-free cells (v), and immune cells (z). Our focus is to find the equilibria of the problem and their stability. The stability of the solutions is of two types: locally asymptotic and globally asymptotic. The Routh–Hurwitz criterion, Volterra-type Lyapunov function, and LaSalle’s invariance principle are used to verify the stability of solutions. The graphical behavior depicts the stable solutions to a real-world problem and supports the stability analysis of the problem. The findings contribute to the understanding of epidemic dynamics and provide valuable information for designing and implementing effective intervention strategies in public health systems.

The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R0. Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelöf technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.

Anthropogenic activities related to mining generate both progress and a vast amount of waste that is responsible for environmental degradation. The Jiu Valley is one of the areas of Romania where mining has affected large areas of land, used to build mines and tailings ponds. The former Coroiesti coal processing plant (CCPP) is such a location with a total area of 25 ha containing approximately 5.5 million tons of tailings. The assessment of the stability of tailings dams is extremely important from safety and environmental aspects. This study proposes a solution based on numerical methods for determining the stability of a section of the dam of a tailings pond. The model of tailings pond no. 1, compartment B, from the Coroieşti Coal Preparation was built using COMSOL Multiphysics. Two scenarios of stability analysis were conducted on a section of the tailings dam: the FOS was determined using the shear strength reduction (SSR) method for both the initial and the current state of this TP. This method is a modern alternative to the limit equilibrium method, and its implementation by COMSOL is new to our country, thus aligning this methodology with current worldwide trends and developments in the field. The results obtained proved to be in line with those calculated in the past with traditional analytical methods, proving that the safety criteria of the studied TP/TD are being met.

In the electrical transmission lines, the processing of cable signals distribution, computer networks, high-speed computer databases and discrete networks can be investigated by the modified Zakharov-Kuznetsov (mZK) equation as a data link propagation control model in the study of nonlinear Schrödinger type equations as well as in the analysis of the generalized stationary Gardner equation. The proposed Gerdjikov–Ivanov model can be used in the field of nonlinear optics, weakly nonlinear dispersion water waves, quantum field theory etc. In this work, we developed complete traveling wave solutions with specific t-type, kink type, bell-type, singular solutions, and periodic singular solutions to the proposed mZK equation and the Gerdjikov-Ivanov equation with the aid of the double G′/G,1/G- expansion method. These settled solutions are very reliable, durable, and authentic which can measure the fluid velocity and fluid density in the electrically conductive fluid and be able to analysis of the flow of current and voltage of long-distance electrical transmission lines too. These traveling wave solutions are available in a closed format and make them easy to use. The proposed method is consistent with the abstraction of traveling wave solutions.

The work is focused on the application of the impedance spectroscopy method to provide evidence and study the effects of aging, temperature, and gas adsorption in chalcogenide-based thin films. The experiments are carried out with thin films of glassy quaternary composition As2Te13Ge8S3 in a wide frequency range at different temperatures under different environmental conditions, in particular, either dry or wet air or their mixtures with NO2 or CO2. It is found that aging has a significant effect on the impedance spectra of Pt–As2Te13Ge8S3–Pt functional structures, which make evidence for the presence of substantial spatial and compositional disordering. This effect can be stabilized by the post-preparation annealing of the sample. The effect of temperature on impedance spectra consists in a variation in the both real and imaginary parts of impedance that appear to be extremely sensitive to adsorptive processes. Adsorption of nitrogen dioxide results in a significant frequency-dependent decrease in the impedance parameters, which is attributed to an effective “strong” chemisorption process due to the interaction of "odd" electrons of NO2 molecules with lone pair electrons of chalcogen atoms. The effect of water vapors leads only to an increase in the real part of impedance, while the imaginary part abruptly decreases; this fact is attributed to a “weak” form of chemisorption. The effect of carbon dioxide on the impedance spectra is attributed to the physical adsorption of CO2 molecules. This effect is weak; however, it is reversible and clearly observed even at room temperature.Lucrarea este dedicată aplicării metodei de spectroscopie a impedanței pentru a oferi dovezi și investigații ale influenței îmbătrânirii, temperaturii și adsorbției gazelor în pelicule subțiri pe bază de calcogenuri amorfe. Experimentele au fost efectuate cu filme subțiri cuaternare sticloase As2Te13Ge8S3 într-o gamă largă de frecvențe, la diferite temperaturi și condiții ambiante, inclusiv aer uscat sau umed, precum și amestecurile lor cu NO2 sau CO2.Sa constatat o influență avansată a îmbătrânirii asupra spectrelor de impedanță ale structurilor funcționale Pt-As2Te13Ge8S3 - Pt, cea ce confirmă prezența unei dezordine spațiale și compoziționale mari ale structurii. Această influență poate fi stabilizată prin tratarea termică a eșantionului. Influența temperaturii asupra spectrelor de impedanță constă în variația părților reale și imaginare ale impedanței care sunt foarte sensibile la procesele de adsorbție. Adsorbția dioxidului de azot, dependent de frecvența câmpului electric aplicat, aduce la o scădere esențială a parametrilor impedanței, ceea ce se explică printr-un proces de chemosorbție „puternic” eficient datorat interacțiunii electronilor „neobișnuiți” ai moleculelor de NO2 cu perechile de electronii solitari ale atomilor de calcogen. Adsorbția vaporilor de apă duce doar la creșterea părții reale a impedanței, pe când partea sa imaginară descrește brusc, explicată printr-o formă „slabă” de chemisorbție. Efectul dioxidului de carbon asupra spectrelor de impedanță este explicat prin adsorbția fizică a moleculelor de CO2. Acest efect este slab, dar este reversibil și clar observat chiar și la temperatura camerei.

Finding optical soliton solutions to nonlinear partial differential equations has become a popular topic in recent decades. The primary goal of this study is to identify a diverse collection of wave solutions to a generalized version of the nonlinear Schrödinger equation. We investigate two modifications to the generalized exponential rational function method to derive the expected results for this model. The first method is primarily based on using elementary functions such as exponential, trigonometric, and hyperbolic forms, which are commonly used to calculate the results. As for the second method, it is based on applying Jacobi elliptic functions to formulate solutions, whereas the underlying idea is the same as with the first method. As a means of enhancing the reader’s understanding of the results, we plot the graphical properties of our solutions. Based on this article’s results, it can be concluded that both techniques are easy to follow, and yet very efficient. These integration methods can determine different categories of solutions all in a unified framework. Therefore, it can be concluded from the manuscript that the approaches adopted in the manuscript may be regarded as efficient tools for determining wave solutions of a variety of partial differential equations. Due to the high computational complexity, the main requirement for applying our proposed methods is to employ an efficient computing software. Here, symbolic packages in Wolfram Mathematica have been used to validate the entire results of the paper.

This research aims to discuss the existence, global stability, periodicity, and bifurcation analysis of a modified version of the ecological model proposed by Tilman and Wedlin [Nature 353, 653–655 (1991)].

The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in microtubules (MTs) are the underlying frameworks to simulate the dynamic features of solitons in optical fibers and the functional aspects of microtubule dynamics. The generalized Kudryashov method is used in this article to extract stable, generic, and wide-ranging soliton solutions, comprising hyperbolic, exponential, trigonometric, and some other functions, and retrieve diverse known soliton structures by balancing the effects of nonlinearity and dispersion. It is established by analysis and graphs that changing the included parameters changes the waveform behavior, which is largely controlled by nonlinearity and dispersion effects. The impact of the other parameters on the wave profile, such as wave speed, wavenumber, etc., has also been covered. The results obtained demonstrate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable soliton solutions to nonlinear evolution equations emerging in various branches of scientific, technological, and engineering domains.

Wearable exoskeleton solutions for upper limb rehabilitation or assistance, particularly for the hand area, have become increasingly attractive to researchers, proving to be effective over time in treating hand movement impairments following various neurological diseases. Our aim in the present work is to design a wearable exoskeleton device for active hand rehabilitation/assist control based on myoelectric signal (EMG) capture from forearm muscles, which is easy to wear by the user, comfortable, lightweight, and relatively inexpensive to make. The actuators use two different lengths to increase biocompatibility with the anatomy of the hand, and PneuNets fluid actuators are used. Their design to meet force and bending requirements was based on finite element numerical simulations, and the actuators were designed based on a clear design methodology to achieve the best possible quality. Tests on healthy subjects show that the EMG-based control strategy meets the needs of rehabilitation/assistive hand therapy, finding a comfortable and easy-to-use device. Future directions will focus on developing the device to meet rehabilitation needs for the entire upper limb and integrating the device into virtual reality (VR) through immersive devices.

In this article, we first consider approach of optical spherical magnetic antiferromagnetic model for spherical magnetic flows of ϒ\Upsilon -magnetic particle with spherical de-Sitter frame in the de-Sitter space S12{{\mathbb{S}}}_{1}^{2}. Hence, we establish new relationship between magnetic total phases and spherical timelike flows in de-Sitter space S12{{\mathbb{S}}}_{1}^{2}. In other words, the applied geometric characterization for the optical magnetic spherical antiferromagnetic spin is performed. Moreover, this approach is very useful to analyze some geometrical and physical classifications belonging to ϒ\Upsilon -particle. Besides, solutions of fractional optical systems are recognized for submitted geometrical designs. Geometrical presentations for fractional solutions are obtained to interpret the model. These obtained results represent that operation is a compatible and significant application to restore optical solutions of some fractional systems. Components of models are described by physical assertions with solutions. Additionally, we get solutions of optical fractional flow equations with designs of our results in de-Sitter space S12{{\mathbb{S}}}_{1}^{2}.

In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge–Kutta method and the non-standard generalized fifth-order Runge–Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies’ simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.

The applications of the diffusion wave model of a time-fractional kind with damping and reaction terms can occur within classical physics. This quantification of the activity can measure the diagnosis of mechanical waves and light waves. The goal of this work is to predict and construct numerical solutions for such a diffusion model based on the uniform cubic B-spline functions. The Caputo time-fractional derivative has been estimated using the standard finite difference technique, whilst, the uniform cubic B-spline functions have been employed to achieve spatial discretization. The convergence of the suggested blueprint is discussed in detail. To assert the efficiency and authenticity of the study, we compute the approximate solutions for a couple of applications of the diffusion model in electromagnetics and fluid dynamics. To show the mathematical simulation, several tables and graphs are shown, and it was found that the graphical representations and their physical explanations describe the behavior of the solutions lucidly. The key benefit of the resultant scheme is that the algorithm is straightforward and makes it simple to implement as utilized in the highlight and conclusion part.

In this article, the Hamiltonian for the conformable harmonic oscillator used in the previous study [Chung WS, Zare S, Hassanabadi H, Maghsoodi E. The effect of fractional calculus on the formation of quantum-mechanical operators. Math Method Appl Sci. 2020;43(11):6950–67.] is written in terms of fractional operators that we called α\alpha -creation and α\alpha -annihilation operators. It is found that these operators have the following influence on the energy states. For a given order α\alpha , the α\alpha -creation operator promotes the state while the α\alpha -annihilation operator demotes the state. The system is then quantized using these creation and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite functions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting α=1\alpha =1.

Doped (with GaCl3), undoped ZnO and ITO/ZnO:Ga nanostructured thin films are synthesized using the spray pyrolysis method. The doped ZnO thin films are synthesized at the atomic ratio of Ga/Zn added in the starting solution fixed at 1, 2, 3, and 5. Gallium-doped ZnO films synthesized on glass/ITO substrates are annealed at 4500C in different environments: vacuum, oxygen, and hydrogen. X-ray diffraction (XRD), Energy-dispersive X-ray spectroscopy (EDX), atomic force microscopy (AFM), and current–voltage (I–V) measurements are applied to characterize the structural properties, composition, surface morphology, and electrical properties of ZnO:Ga nanostructured thin films. X-ray diffraction analysis shows that ZnO:Ga films deposited on glass substrates have a dense and homogeneous surface with a hexagonal structure. The ZnO:Ga films deposited on glass/ITO substrates are composed of two phases, namely, hexagonal ZnO and cubic ITO. The I–V characteristics show the presence of good ohmic contacts between Al and In metals and ZnO:Ga thin films regardless of the nature of the substrate and the annealing atmosphere.Au fost sintetizate straturi subțiri nanostructurate ZnO atât dopate cu (GaCl3), cât și nedopate, precum și straturi de ITO/ZnO:Ga, folosind metoda prin pulverizare cu piroliză. Straturile subțiri de ZnO dopate au fost sintetizate la raportul atomic Ga/Zn adăugat în soluția inițială fixă la 1, 2, 3 și 5 Straturile nanostructurate de ZnO dopate cu Ga obținute pe substraturi de sticlă/ITO au fost tratate termic la 450℃ în diferite medii: vid, oxigen și hidrogen. S-au realizat măsurătorile de difracție cu raze X (XRD), spectroscopie cu raze X cu dispersie energetică (EDX), microscopie cu forță atomică (AFM), curent-tensiune (I-V) pentru a caracteriza proprietățile structurale, compoziția, morfologia suprafeței și proprietățile electrice ale straturilor subțiri de ZnO:Ga. Analiza XRD arată că stratul de ZnO:Ga depus pe substratul de sticlă are o suprafață densă și omogenă cu structura hexagonală. Stratul de ZnO:Ga depus pe substraturi de sticlă/ITO indică două faze, acestea fiind ZnO hexagonal și ITO cubic. Caracteristica I-V prezintă contacte ohmice bune între metalele Al, In și straturile subțiri de ZnO:Ga, indiferent de natura substratului și de atmosfera de tratare termică.

In this paper, a p–n thin film NiO/ZnO heterojunction for a rectifier diode and a UV photodetector is prepared and characterized. Nickel oxide (NiO) and gallium-doped zinc oxide (ZnO:Ga) thin films are grown by RF magnetron sputtering and spray pyrolysis techniques, respectively. The crystal structure of the thin films is studied by the X-ray diffraction (XRD) method. The transmittance and reflectance are studied by UV–VIS spectroscopy. The p–n electrical parameters are estimated from current–voltage characteristics. The effects of duration of thermal annealing at 450oC on the characteristics of the NiO/ZnO:Ga device are evaluated. The non-annealed diode shows the best rectification coefficient of 105 at ±1 V. The p–n photodetection capability is studied under UV illumination. At a reverse bias of –3 V under 365-nm UV illumination, the device shows a current intensity of ~6.2 × 10-12 A. The observed increase in the reverse current intensity by about two orders of magnitude under a UV lamp with a spectral irradiance of 10 W m-2 μ m-1 indicates a promising application in UV light detection.În această lucrare, a fost descrisă fabricarea și caracterizarea diodei redresoare și senzorului UV pe baza heterojoncțiunii cu straturi subțiri p-NiO/n-ZnO. Straturile subțiri de oxid de nichel (NiO) și oxid de zinc (ZnO:Ga) au fost obținute prin metoda pulverizării în regim de radiofrecvenţă (RF) și, respectiv, metoda pulverizării pirolitice. Structura cristalină a straturilor subțiri a fost investigată prin metoda difracției cu raze X (XRD). Transmitanța și reflectanța au fost studiate prin spectroscopie UV-VIS. Parametrii electrici ai heterojoncțiunii p-n au fost estimați din caracteristicile curent-tensiune. Au fost evaluate efectele duratei tratării termice la 450oC asupra caracteristicilor structurii NiO/ZnO:Ga. Dioda redresoare netratată a arătat cel mai bun coeficient de redresare de 105 la aplicarea tensiunii ±1 V. Capacitatea de detecție a senzorului pe baza heterojoncțiunii p-n a fost studiată la iluminarea UV. Curentul de întuneric al joncțiunii la polarizare inversă de -3V este ~ 6,2 × 10-12 A. O creștere a curentului invers cu aproximativ două ordine de mărime la iluminare cu lampa UV cu iradiere spectrală 10 Wm-2aproximativ două ordine de mărime la iluminare cu lampa UV cu iradiere spectrală 10 Wm-2aproximativ două ordine de mărime la iluminare cu lampa UV cu iradiere spectrală 10 Wm-2 μ m-1 prezintă o aplicație promițătoare în detectarea luminii UV.m-1 prezintă o aplicație promițătoare în detectarea luminii UV.m-1 prezintă o aplicație promițătoare în detectarea luminii UV.

In this research, we expose new results on the dynamics of a high disturbed chemostat model for industrial wastewater. Due to the complexity of heavy and erratic environmental variations, we take into consideration the polynomial perturbation. We scout the asymptotic characterization of our proposed system with a general interference response. It is demonstrated that the long-run characteristics of the chemostat process are classified by using the threshold classification approach. If the critical sill is strictly negative, the bacteria will disappear exponentially, indicating that the chemostat wastewater process is not running (excluded scenario), otherwise, the stationarity and ergodicity properties of our model are verified (practical scenario). The theoretical arsenal of this work offers a comprehensive overview of the industrial wastewater behavior under general hypotheses and introduces novel technical aspects to deal with other perturbed systems in biology. Numerically, we audit the accuracy of our threshold in three particular situations: linear, quadratic and cubic perturbations. We establish that the increasing order of disturbance has a passive influence on the extinction time of bacteria. This finding highlights that complex noise sources fulfill a significant role in the transient dynamics of chemostat systems.

The general time fractional Burger- Fisher (TF-BF) and the space–time regularized long-wave (STF-RLW) equations are considered as examples of gravitational water waves in cold plasma as well as so many areas. The above equations are used in nonlinear science and engineering to study long waves in seas and harbors that travel in just one direction. First, the two equations are transformed to ODEs by applying a fractional complex transform along with characteristics of confirmable fractional derivative (CFD). Then, the extended tanh-function (ET-F) approach is investigated to find a variety of analytical solutions with different geometrical wave structures the mentioned models. The results are in the form of kink, one-, two-, multiple-solitons solutions, and other types sketched in 2D, 3D, and contour patterns.

This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is revealed to be grounded on six basic precepts. But one finds that all the respective precepts are discredited by insurmountable deficiencies. So, in regard to UR, the alluded philosophy discloses oneself to be an unjustified mythology. Then UR appear either as short-lived historical conventions or as simple and limited mathematical formulas, without any essential significance for physics. Such a finding reinforces the Dirac's prediction that UR 'in their present form will not survive in the physics of future'. The noted facets of UR motivate reconsiderations of associated debates on QMS. Mainly one reveals that, properly, UR have not any essential connection with genuine descriptions of QMS. For such descriptions, it is necessary that, mathematically, the quantum observables to be considered as random variables. The measuring scenarios with a single sampling, such are wave function collapse or Schrodinger's cat thought experiment, are revealed as being useless inventions. We propose to describe QMS as transmission processes for stochastic data. Note that, for existing quantum debates, the above UR-QMS revaluations, offer a few arguments for lucrative parsimony in approaches of matters. The unlucrative aspects of those debates have to be reconsidered too, probably in more or less speculative visions., Motto 1: 'I think one can make a safe guess that uncertainty relations in their present form will not survive in the physics of future.' P. A. M. Dirac, 1963 [...]

The aim of this article was to address the lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation with the aid of Hirota bilinear technique. This model concerns in a massive nematic liquid crystal director field. By choosing the function f in Hirota bilinear form, as the general quadratic function, trigonometric function and exponential function along with appropriate set of parameters, we find the lump, lump-one stripe, multiwave and breather solutions successfully. We also interpreted some three-dimensional and contour profiles to anticipate the wave dynamics. These newly obtained solutions have some arbitrary constants and so can be applicable to explain diversity in qualitative features of wave phenomena.

In this article, a modified variational iteration method along with Laplace transformation is used for obtaining the solution of fractional-order nonlinear convection–diffusion equations (CDEs). The proposed technique is applied for the first time to solve fractional-order nonlinear CDEs and attain a series-form solution with the quick rate of convergence. Tabular and graphical representations are presented to confirm the reliability of the suggested technique. The solutions are calculated for fractional as well as for integer orders of the problems. The solution graphs of the solutions at various fractional derivatives are plotted. The accuracy is measured in terms of absolute error. The higher degree of accuracy is observed from the table and figures. It is further investigated that fractional solutions have the convergence behavior toward the solution at integer order. The applicability of the present technique is verified by illustrative examples. The simple and effective procedure of the current technique supports its implementation to solve other nonlinear fractional problems in different areas of applied science.

In this article, exact solutions of some Laplace-type fractional boundary value problems (FBVPs) are investigated via natural decomposition method. The fractional derivatives are described within Caputo operator. The natural decomposition technique is applied for the first time to boundary value problems (BVPs) and found to be an excellent tool to solve the suggested problems. The graphical representation of the exact and derived results is presented to show the reliability of the suggested technique. The present study is mainly concerned with the approximate analytical solutions of some FBVPs. Moreover, the solution graphs have shown that the actual and approximate solutions are very closed to each other. The comparison of the proposed and variational iteration methods is done for integer-order problems. The comparison, support strong relationship between the results of the suggested techniques. The overall analysis and the results obtained have confirmed the effectiveness and the simple procedure of natural decomposition technique for obtaining the solution of BVPs.