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Aim of the present study: It must study liquid flow over surfaces above the earth because its surface rotation stimulates liquids heated amid the sun. Consequently, the Coriolis impact force is investigated on Casson convective flow fluid with Cattaneo-Christov heat flux over the rotating paraboloid upper surface. Significance of the present study: The simultaneous effects of the Lorentz force and Coriolis force occurring due to MHD flow contribute significantly to solar wind, sunspots, and more physical natural phenomena. As a result, Navier-Stokes equations governing the flow are derived and incorporated with the appropriate body forces. Methodology: PDEs are converted to ODEs by identical variants/variables that make the governing equations non-dimensional. The results of this problem are represented graphically using BVP4C. Conclusion: In the present study, some of the significant results are: While both ANN and ANFIS-PSO could accurately forecast the truth values, we found that ANFIS-PSO is more accurate; as the temperature rises, β and Gr consider and resist heat transmission with K and Ec, While Ec and Nt increase the concentration, K, β, Gr, Nb, and Sc impede mass transfer. table 3 compares the current study's findings with those of the previous research; the results are nearly identical, demonstrating the precision and accuracy of the current model.

In this paper, we improved recent results on the existence of solutions for nonlinear fractional boundary value problems containing the Atangana-Baleanu fractional derivative of order $ \zeta \in (1, 2) $. We also derived the exact relations between these fractional boundary value problems and the corresponding fractional integral equations in infinite dimensional Banach spaces. We showed that the continuity assumption on the nonlinear term of these equations is insufficient, give the derived expression for the solution, and present two results about the existence and uniqueness of the solution. We examined the case of impulsive impact and provide some sufficiency conditions for the existence and uniqueness of the solution in these cases. We also demonstrated the existence and uniqueness of anti-periodic solution for the studied problems and considered the problem when the right-hand side was a multivalued function. Examples were given to illustrate the obtained results.

This paper examines the stability behavior of the nonlinear dynamical motion of a vibrating cart with two degrees of freedom (DOFs). Lagrange’s equations are employed to establish the mechanical regulating system of the examined motion. The proposed approximate solutions (ASs) of this system are estimated through the use of the multiple-scales method (MSM). These solutions are considered novel as the MSM is being applied to a new dynamical model. Secular terms have been eliminated to meet the solvability criteria, and every instance of resonance that arises is categorized, where two of them are examined concurrently. Therefore, the modulation equations are developed based on the representations of the unknown complex function in polar form. The solutions for the steady state are calculated using the corresponding fixed points. The achieved solutions are displayed graphically to illustrate the impact of manipulating the system’s parameters and are compared to the numerical solutions (NSs) of the system’s original equations. This comparison shows a great deal of consistency with the numerical solution, which indicates the accuracy of the applied method. The nonlinear stability criteria of Routh–Hurwitz are employed to assess the stability and instability zones. The value of the proposed model is exhibited by its wide range of applications involving ship motion, swaying architecture, transportation infrastructure, and rotor dynamics.

The aim of this work is to study some asymptotic properties of a class of third-order advanced differential equations. We present new oscillation criteria that complete, simplify and improve some previous results. We also provide many different examples to clarify the significance of our results.

The aim of this paper is to derive conditions under which the solution set of a non-local impulsive differential inclusions involving Atangana-Baleanu fractional derivative is a nonempty compact set in an infinite dimensional Banach spaces. Existence results for solutions in the presence of instantaneous or non-instantaneous impulsive effect are given. We considered the case where the right hand side is either a single valued function, or a multifunction. This generalizes recent results to the case when there are impulses, the right hand side is a multifunction, and where the dimension of the space is infinite. Examples are given to illustrate the effectiveness of the established results.

This study explores the effects of using space-fractional derivatives and adding multiplicative noise, modeled by a Wiener process, on the solutions of the space-fractional stochastic regularized long wave equation. New fractional stochastic solutions are constructed, and the consistency of the obtained solutions is examined using the transition between phase plane orbits. Their bifurcation and dependence on initial conditions are investigated. Some of these solutions are shown graphically, illustrating both the individual and combined influences of fractional order and noise on selected solutions. These effects appear as alterations in the amplitude and width of the solutions, and as variations in their smoothness.

The fungus Fusarium oxysporum (f.sp. albedinis) causes Bayoud disease. It is one of the epiphytotic diseases that affects a wide range of palm species and has no known cure at present. However, preventive measures can be taken to reduce the effects of the disease. Bayoud disease has caused enormous economic losses due to decreased crop yield and quality. Therefore, it is essential to develop a mathematical model for the dynamics of the disease to propose some affordable methods for disease management. In this study, we propose a novel mathematical model that describes the transmission dynamics of the disease in date palm trees. The model incorporates various factors such as the contact rate of the fungi with date palm trees, the utilization of fungicides, and the introduction of a quarantine compartment to prevent disease dissemination. We first prove a few key properties of the proposed model to ensure that the model is well-posed and suitable for numerical investigations. We establish that the model has a unique positive solution that is bounded and stable over time. We use sensitivity analysis to identify the parameters that have the greatest effect on the reproduction number R0 and illustrate this effect graphically. We then formulate an optimal control problem to identify the most suitable and cost-effective disease control approaches. As a first approach, we solely focus on the application of fungicide to susceptible trees and determine the best spray rates for a greater decrease in exposed and infected trees. Secondly, we emphasize quarantining exposed and infected trees at optimal quarantine rates. Finally, we explore the combined effect of fungicide spraying and isolating infected trees on disease control. The findings of the last approach turn out to be the most rewarding and cost-effective for minimizing infections in date palm trees.

This paper presents a hybrid based nanofluid flow past over a stretching/shrinking surface. The magnetic field effect is applied normal to the surface. Additionally, the melting heat transfer effect is also taken into considerations. For the performance of heat transport phenomenon, the heat generation/absorption effect is added. The suitable similarity transformations are used to transform the partial differential equations into dimensionless form of ordinary differential equations. For obtaining solutions of the problem, a bvp4c technique is used to handle the transformed differential equations along with boundary conditions. Dual nature study is performed which is the first and second solutions of the problem. In the first solution, increasing the melting temperature improves the rate of heat transfer. Higher values of the shrinking parameter cause an increase in the velocity profile in the first solution and decreases in the second solution. Further, the temperature of the liquid improves as the thermal radiation and heat generation parameters increase, respectively. The temporal stability analysis represents that only one of the two solutions is stable as time evolves. The numerical results are acquired in the form of tabulated data and graphical structures.

This study reveals a Maxwell nanofluid flow with the effect of activation energy. The flow is generated by a stretching as well as swirling of the disk. For the formulation of heat transport mechanism, the Fourier's law of heat conduction is used with the addition of heat generation/absorption and thermal radiation. The von Karman's variables are employed to convert the partial differential equations (PDEs) into non-dimensional ordinary differential equations (ODEs). The numerical procedure is utilized in order to investigate the governing problem by a bvp midrich technique in Maple software. The involved different physical parameters are discussed through graphs and tables. Results reveal that the velocity enhances in the radial component and reduces in the azimuthal component. Further, the thermal profile enhances with the impact of thermal radiation and heat generation parameters, respectively.

The current work is devoted to studying the dynamical behavior of the Sakovich equation with beta derivatives. We announce the conditions of problem parameters leading to the existence of periodic, solitary, and kink solutions by applying the qualitative theory of planar dynamical systems. Based on these conditions, we construct some new solutions by integrating the conserved quantity along the possible interval of real wave propagation in order to obtain real solutions that are significant and desirable in real-world applications. We illustrate the dependence of the solutions on the initial conditions by examining the phase plane orbit. We graphically show the fractional order beta effects on the width of the solutions and keep their amplitude approximately unchanged. The graphical representations of some 3D and 2D solutions are introduced.

The COVID-19 pandemic has become a worldwide concern and has caused great frustration in the human community. Governments all over the world are struggling to combat the disease. In an effort to understand and address the situation, we conduct a thorough study of a COVID-19 model that provides insights into the dynamics of the disease. For this, we propose a new LSHSEAIHR COVID-19 model, where susceptible populations are divided into two sub-classes: low-risk susceptible populations, LS, and high-risk susceptible populations, HS. The aim of the subdivision of susceptible populations is to construct a model that is more reliable and realistic for disease control. We first prove the existence of a unique solution to the purposed model with the help of fundamental theorems of functional analysis and show that the solution lies in an invariant region. We compute the basic reproduction number and describe constraints that ensure the local and global asymptotic stability at equilibrium points. A sensitivity analysis is also carried out to identify the model’s most influential parameters. Next, as a disease transmission control technique, a class of isolation is added to the intended LSHSEAIHR model. We suggest simple fixed controls through the adjustment of quarantine rates as a first control technique. To reduce the spread of COVID-19 as well as to minimize the cost functional, we constitute an optimal control problem and develop necessary conditions using Pontryagin’s maximum principle. Finally, numerical simulations with and without controls are presented to demonstrate the efficiency and efficacy of the optimal control approach. The optimal control approach is also compared with an approach where the state model is solved numerically with different time-independent controls. The numerical results, which exhibit dynamical behavior of the COVID-19 system under the influence of various parameters, suggest that the implemented strategies, particularly the quarantine of infectious individuals, are effective in significantly reducing the number of infected individuals and achieving herd immunity.

In this paper, we investigate the time M-fractional modified nonlinear Schrödinger equation that describes the propagation of rogue waves in deep water. Periodic, solitary, and kink (or anti-kink) wave solutions are discussed using the bifurcation theory for planar integrable systems. Some new wave solutions are constructed using the first integral for the traveling wave system. The degeneracy of the obtained solutions is investigated by using the transition between orbits. We visually explore some of the solutions using graphical representations for different values of the fractional order.

In this study, an advanced computational artificial neural network (ANN) procedure is designed using the novel characteristics of the Levenberg–Marquardt backpropagation (LBMBP), i.e., ANN-LBMBP, for solving the waste plastic management in the ocean system that plays an important role in the economy of any country. The nonlinear mathematical form of the waste plastic management in the ocean system is categorized into three groups: waste plastic material W(χ), marine debris M(χ), and reprocess or recycle R(χ). The learning based on the stochastic ANN-LBMBP procedures for solving mathematical waste plastic management in the ocean is used to authenticate the sample statics, testing, certification, and training. Three different statistics for the model are considered as training 70%, while for both validation and testing are 15%. To observe the performances of the mathematical model, a reference dataset using the Adams method is designed. To reduce the mean square error (MSE) values, the numerical performances through the ANN-LBMBP procedures are obtained. The accuracy of the designed ANN-LBMBP procedures is observed using the absolute error. The capability, precision, steadfastness, and aptitude of the ANN-LBMBP procedures are accomplished based on the multiple topographies of the correlation and MSE.

The qualitative theory for planar dynamical systems is used to study the bifurcation of the wave solutions for the space-fractional nonlinear Schrödinger equation with multiplicative white noise. Employing the first integral, we introduce some new wave solutions, assorted into periodic, solitary, and kink wave solutions. The dependence of the solutions on the initial conditions is investigated. Some solutions are clarified by the display of their 2D and 3D representations with varying levels of noise to show the influence of multiplicative white noise on the solutions.

In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand the dynamic behavior of COVID-19. For the dynamic study, a new SEIAPHR fractional model was purposed in which infectious individuals were divided into three sub-compartments. The purpose is to construct a more reliable and realistic model for a complete mathematical and computational analysis and design of different control strategies for the proposed Caputo–Fabrizio fractional model. We prove the existence and uniqueness of solutions by employing well-known theorems of fractional calculus and functional analyses. The positivity and boundedness of the solutions are proved using the fractional-order properties of the Laplace transformation. The basic reproduction number for the model is computed using a next-generation technique to handle the future dynamics of the pandemic. The local–global stability of the model was also investigated at each equilibrium point. We propose basic fixed controls through manipulation of quarantine rates and formulate an optimal control problem to find the best controls (quarantine rates) employed on infected, asymptomatic, and “superspreader” humans, respectively, to restrict the spread of the disease. For the numerical solution of the fractional model, a computationally efficient Adams–Bashforth method is presented. A fractional-order optimal control problem and the associated optimality conditions of Pontryagin maximum principle are discussed in order to optimally reduce the number of infected, asymptomatic, and superspreader humans. The obtained numerical results are discussed and shown through graphs.

This work aims to explore some dynamic aspects of the problem of star motion that is impacted by the rotation of the galaxy, which we model as a bisymmetric potential based on a two-dimensional harmonic oscillator with sextic perturbations. We demonstrate analytically that the motion is non-integrable when certain conditions are met. The analytical results for the non-integrability are confirmed by showing the irregularity of the behavior of the motion through utilizing the Poincaré surface of a section as a numerical method. The motion equilibrium positions are detected, and their stability is discussed. We show that the force generated by the rotating frame acts as a stabilizer for the maximum equilibrium points. We display graphically that the size of the stability regions relies on the angular velocity magnitude for the frame. Through the application of Lyapunov’s theorem, periodic solutions can be constructed which are close to the equilibrium positions. Furthermore, we demonstrate that there are one or two families of periodic solutions relying on whether the equilibrium point is a saddle or stable, respectively.

In this paper, we provide an algorithm for verifying the validity of identities of the form ∑A⊆n¯cA‖xA‖2=0, where xA=∑i∈Axi and n¯={1,⋯,n} in inner-product spaces. Such algorithm is used to verify the validity, in inner-product spaces, for a number of identities. These include a generalization of the parallelepiped law. We also show that such identities hold only in inner-product spaces. Thus, the algorithm can be used to deduce characterizations of inner-product spaces.

In this study, an analysis of the rotating flow of viscoelastic Oldroyd-B fluid along with porous medium featuring the Soret–Dufour effects is explored. The heat transport mechanism is discussed with the involvement of thermal radiation and heat source/sink. Additionally, the thermophoresis of particle deposition and chemical reaction are taken into the concentration equation in order to investigate the mass transportation in the liquid. To formulate the non-linear ordinary differential equations, the von Karman similarity approach is used in the system of partial differential equations and then integrated numerically by the bvp midrich scheme in Maple programming. Results are provided by graphical framework and tabular form. A quick parametric survey is carried out concerning flow field, thermal, and solutal distributions through graph representation. The curves show that increasing the values of the retardation time parameter decreases the radial velocity while increasing the angular velocity. Additionally, when the relaxation time parameter becomes powerful, the magnitude of the velocity curves decreases considerably in the radial and axial directions. The presence of a radiation parameter indicates that the fluid will absorb a greater amount of heat, which is equivalent to a higher temperature. Further, an increase in the stretching parameter leads to a reduction in the temperature components.

The purpose of this study is to provide a mathematical construction based on the novel singular perturbed model of the second kind (NSPM-SK) using the standard form of the Lane–Emden. The singular Lane–Emden types of the models have abundant applications in astrophysics. The inclusive features of this model are provided using the perturbed, pantograph, singular point together and the shape factor based on the NSPM-SK. These models become more complicated by using these factors through the artificial neural networks (ANNs) together with the optimization procedures of the swarming particle swarm optimization (PSO) paradigms and the local sequential quadratic programming (SQP). An objective function is provided based on the differential form of the NSPM-SK and then optimization is performed through the hybridization of the PSOSQP. The exactness of the model is attained to solve three different variations of the mathematical NSPM-SK by using the overlapping of the obtained and true results. The stability, robustness, and convergence of the designed numerical approach are perceived by using different statistical performances of the ANNs together with the optimization of the PSOSQP for 30 independent executions.

This paper focuses on the implementation of an accurate meshless scheme for the simulation of the advection–diffusion of non-active pollutant in a two-dimensional depth-averaged flow. The depth-averaged flow model includes the shallow water system and the pollutant propagation described by the advection–diffusion equation with diffusion tensor. The mathematical model was implemented by using a meshless method based on local radial basis functions. This method was used to numerically evaluate the spatial derivatives and complemented with the second-order Runge–Kutta method for the time evolution. To remove the non-physical oscillations, which appear at the discontinuity, a filter based on a hyperviscosity operator was applied. To investigate the effectiveness and accuracy of the proposed scheme, a number of tests are presented, including the dam break problem, and the pure transport of a pollutant in a long channel. Finally, a hypothetical example of a pollutant transport in the Strait of Gibraltar is modeled. The results obtained are compared both with analytical solutions and with simulation results obtained by a finite volume method based on the Roe-MUSCL scheme. The main advantages of the proposed method are: (i) the simplicity of implementation, (ii) the ability to handle calculations of slowly varying flows or concentrations, as well as rapidly varying flows containing shocks or discontinuities, and (iii) the ability to satisfy the C-property and guarantee positive values of both water level and pollutant concentration.

A numerical study is conducted to evaluate the steady natural convective heat transfer problem and entropy generation of both single wall (SWCNT) and multi wall (MWCNT) nanoparticles with water as a base liquid over two spaced spheres. The isothermally heated spheres are located between two plates of short length. The cooled plates are maintained at different inclination angles. A numerical approach based on the finite volume method and multigrid acceleration was used to solve the governing equations. The effects of nanoparticle type, volume fraction, the inclination angle of the plates and the Rayleigh numbers are well-considered. Results reveal that there is a remarkable enhancement of the average Nusselt number over the plates for MWCNT nanoparticles with 63.15% from the inclination angle 0° to 30°. Furthermore, optimal heat transfer rates over the plates for MWCNT nanoparticles equates to 1.9, which is obtained for the inclination 30° and a Rayleigh number of 106. However, for SWCNT nanoparticles, the same equates 0.9, which is obtained for the inclination 90° and a Rayleigh number of 106. The comprehensive analysis is presented under some well-defined assumptions which show the reliability of the present investigation.

This manuscript optimizes the conjugate heat transfer and thermal-stress analysis for hydromagnetic Brinkman fluid with chemical reaction in permeable media. The governing equations of non-Newtonian Brinkman fluid have been traced out and then fractional derivative approach, namely, Caputo–Fabrizio, is invoked, subject to the exponential boundary conditions. The Fourier Sine and Laplace transforms are applied on governing partial differential equations for generating the analytical results of temperature, concentration and velocity. A comparative study of velocity field is investigated for the sake of long memory and hereditary properties. The analytical investigation of temperature, concentration and velocity field have strong effects on chemical reaction. The graphical depiction of vibrant characteristics of hydromagnetic Brinkman fluid with chemical reaction in permeable media is exhibited for disclosing the sensitivities of different embedded rheological parameters of fluid flow. The results suggested that temperature distribution for smaller and larger Prandtl number has disclosed quick and thicker heat diffusivity.

The study of gold nanoparticles (AuNPs) in the blood flow has emerged as an area of interest for numerous researchers, due to its many biomedical applications, such as cancer radiotherapy, DNA and antigens, drug and gene delivery, in vitro evaluation, optical bioimaging, radio sensitization and laser phototherapy of cancer cells and tumors. Gold nanoparticles can be amalgamated in various shapes and sizes. Due to this reason, gold nanoparticles can be diffused efficiently, target the diseased cells and destroy them. The current work studies the effect of gold nanoparticles of different shapes on the electro-magneto-hydrodynamic (EMHD) peristaltic propulsion of blood in a micro-channel under various effects, such as activation energy, bioconvection, radiation and gyrotactic microorganisms. Four kinds of nanoparticle shapes, namely bricks, cylinders and platelets, are considered. The governing equations are simplified under the approximations of low Reynolds number (LRN), long wavelength (LWL) and Debye–Hückel linearization (DHL). The numerical solutions for the non-dimensional equations are solved using the computational software MATLAB with the help of the bvp4c function. The influences of different physical parameters on the flow and thermal characteristics are computed through pictorial interpretations.

There is no denying fact that nanoparticles of carbon nanotubes are employed to improve the performance of thermal stability in comparison with traditional nanoparticles, this is because nanoparticles of carbon nanotubes possess outstanding material properties. In this manuscript, a mathematical model of mixed convective flow based on carbon nanotubes suspended in ethylene glycol has been developed and derived by means of Fourier Sine transform. In order to analyze the thermophysical properties of nanofluid, the temperature and velocity profiles have been investigated through fractional derivative and integral transforms. The comparative analysis of single and multi-walled carbon nanotubes has been presented for the sake of enhancement of heat transfer. It is worth mentioning that embedded rheological parameters have shown the sensitivity for the enhancement of heat transfer with and without fractional techniques through graphical illustration.

This numerical investigation presents the effects of the position of baffles in the shape of a circle’s segment placed inside a circular channel to improve the thermal and flow performance of a solar air heater. Three different baffles’ positions with Reynolds number varying between 10,000 to 50,000 were investigated computationally. The k-omega SST model was used for solving the governing equations. Air was taken as the working fluid. Three pitch ratios (Y = 3, 4, and 5) were considered, while the height of the baffles remained fixed. The result showed an enhancement in Nusselt number, friction factor, j-factor, and thermal performance factor. Staggered exit-length baffles showed maximum enhancement in heat transfer and pressure drop, while inline inlet-length baffles showed the least enhancement. For a pitch ratio of Y = 3.0, the enhancement in all parameters was the highest, while for Y = 5.0, the enhancement in all parameters was the least. The highest thermal performance factor of 1.6 was found for SEL at Y = 3.0.