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The heat transfer ratio has an important role in industry and the engineering sector; the heat transfer ratios of CNT nanofluids are high compared to other nanofluids. This paper examines the analytical investigation of the time-dependent stagnation point flow of a CNT nanofluid over a stretching surface. For the investigation of the various physical restrictions, single and multi-walled carbon nanotubes (SWCNTs, MWCNTs) were used and compared. The defined similarity transformation was used, to reduce the given nonlinear partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). The model nonlinear ordinary differential equations were solved, with an approximate analytical (OHAM) optimal homotopy asymptotic method being used for the model problem. The impact of different parameters such as magnetic field parameter, unsteady parameter, dimensionless nanoparticles volume friction, Prandtl number, and Eckert number are interpreted using graphs, in the form of the velocity and temperature profile. [ABSTRACT FROM AUTHOR]

Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm. [ABSTRACT FROM AUTHOR]

A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New analytical solutions to the distributed-order fractional diffusion–wave equation are determined using the Laplace and Dirichlet-Weber integral transforms. The influence of the fractional parameters on the radial groundwater flow is analyzed by numerical calculations and graphical illustrations are obtained with the software Mathcad. [ABSTRACT FROM AUTHOR]

The model developed in this study presents a mathematical approach to the physiological transport of seminal liquid due to ciliary movements, which are attached with the lumen of the ductile efferent in the male reproductive system. The rheological properties of the seminal liquids were described using the Jeffrey liquid model. The problem described an electromagnetic mixed convective flow of a Jeffrey liquid through a vertical channel with heat and mass transfers. The effects of chemical reactions and the external heat generation were included in the formulation. The flow took place through an active porous medium (due to thick cilia mat and other deposits) and was influenced by the Lorentz magnetic force. Four basic conservation laws of mass, momentum, energy, and concentration were utilized in the mathematical modeling. These are highly nonlinear equations, which were simplified due to a physiologically valid approach known as LAT (lubrication approximation theory). Analytical solutions for temperature, concentration, and velocity profiles were evaluated. The expressions describing the pressure–volume flow rate relationships were also obtained. Analysis of various physical and geometrical factors affecting the pressure–volume (pumping) characteristics was also presented. One of the main findings of our study is that the difference between our calculated values of the flow rate and the estimated values of the flow rate in the ductile efferent was negligibly small. Moreover, our results can be implemented in the artificial cilia pumping systems in microchannels. [ABSTRACT FROM AUTHOR]

In the present research work, a newly developed technique which is known as variational homotopy perturbation transform method is implemented to solve fractional-order acoustic wave equations. The basic idea behind the present research work is to extend the variational homotopy perturbation method to variational homotopy perturbation transform method. The proposed scheme has confirmed, that it is an accurate and straightforward technique to solve fractional-order partial differential equations. The validity of the method is verified with the help of some illustrative examples. The obtained solutions have shown close contact with the exact solutions. Furthermore, the highest degree of accuracy has been achieved by the suggested method. In fact, the present method can be considered as one of the best analytical techniques compared to other analytical techniques to solve non-linear fractional partial differential equations. [ABSTRACT FROM AUTHOR]

In this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by using the suggested method which provides the desired rate of convergence. Some numerical examples are solved by using the proposed method. The solutions of the targeted problems are represented by graphs which have confirmed closed contact between the exact and obtained solutions of the problems. Based on the novelty and straightforward implementation of the method, it is considered to be one of the best analytical techniques to solve linear and non-linear fractional partial differential equations. [ABSTRACT FROM AUTHOR]

Nanoscience can be stated as a superlative way of changing the properties of a working fluid. Heat transmission features during the flow of nanofluids are an imperative rule from the industrial and technological point of view. This article presents a thin film flow of viscous nanofluids over a horizontal rotating disk. The impact of non-linear thermal radiation and a uniform magnetic field is emphasized in this work. The governing equations were transformed and solved by the homotopy analysis method and the ND-Solve technique. Both analytical and numerical results are compared graphically and numerically, and excellent agreement was obtained. Skin friction and the Nusselt number were calculated numerically. It is concluded that the thin film thickness of nanofluids reduces with enhanced values of the magnetic parameter. In addition, the nanofluid temperature was augmented with increasing values of the thermal radiation parameter. The impact of emerging parameters on velocities and temperature profiles were obtainable through graphs and were deliberated on in detail. [ABSTRACT FROM AUTHOR]

Cancer is a prominent source of mortality and morbidity globally, but little is known about how it develops and spreads. Tumor cells are unable to thrive in high-temperature environments, according to recent research. Hyperthermia is the name for this therapy method. This study provides insights into hyperthermia therapy on breast cancer in the presence of a porous material with fractional derivative access when using radiative microwave heating. The mathematical model is formulated by PDE, while the time-fractional Caputo derivative is applied to make our equation more general as compared to the classical model. To produce a more efficient analysis of blood temperature distributions inside the tissues of the breast, the unsteady state is calculated by using the Laplace transform technique. The Laplace inversion is found by Durbin's and Zakian's algorithms. The treatment involves mild temperature hyperthermia, which causes cell death by enhancing cell sensitivity to radiation therapy and blood flow in the tumor. The variations of different parameters to control the temperate profile during therapy are discussed; we can also see how a fractional parameter makes our study more realistic for further experimental study. [ABSTRACT FROM AUTHOR]

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear "partial" differential equations (PDEs) into a system of nonlinear "ordinary" differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model's answers. This method may be expanded to solve additional physical issues with complicated geometry. [ABSTRACT FROM AUTHOR]

This research work aims to scrutinize the mathematical model for the hybrid nanofluid flow in a converging and diverging channel. Titanium dioxide and silver T i O 2   and   A g are considered as solid nanoparticles while blood is considered a base solvent. The couple-stress fluid model is essentially use to describe the blood flow. Therefore, the couple-stress term was used in the recent study with the existence of a magnetic field and a Darcy–Forchheiner porous medium. The heat absorption/omission and radiation terms were also included in the energy equation for the sustainability of drug delivery. An endeavor was made to link the recent study with the applications of drug delivery. It has already been revealed by the available literature that the combination of T i O 2 with any other metal can destroy cancer cells more effectively than T i O 2 separately. Both the walls are stretchable/shrinkable, whereas flow is caused by a source or sink with α as a converging/diverging parameter. Governing equations were altered into the system of non-linear coupled equations by using the similarity variables. The homotopy analysis method (HAM) was applied to obtain the preferred solution. The influences of the modeled parameters have been calculated and displayed. The confrontation of wall shear stress and hybrid nanofluid flow increased as the couple stress parameter rose, which indicates an improvement in the stability of the base fluid (blood). The percentage (%) increase in the heat transfer rate with the variation of nanoparticle volume fraction was also calculated numerically and discussed theoretically. [ABSTRACT FROM AUTHOR]

Because of the floating magnetic nanomaterial, ferrofluids have magneto-viscous properties, enabling controllable temperature changes as well as nano-structured fluid characteristics. The study's purpose is to evolve and solve a theoretical model of bioconvection nanofluid flow with a magnetic dipole effect in the presence of Curie temperature and using the Forchheimer-extended Darcy law subjected to a vertical cone surface. The model also includes the nonlinear thermal radiation, heat suction/injection, viscous dissipation, and chemical reaction effects. The developed model problem is transformed into nonlinear ordinary differentials, which have been solved using the homotopy analysis technique. In this problem, the behavior of function profiles are graphically depicted and explained for a variety of key parameters. For a given set of parameters, tables representthe expected numerical values and behaviors of physical quantities. The nanofluid velocity decreases as the ferrohydrodynamic, local inertia, and porosity parameters increase and decrease when the bioconvection Rayleigh number increases. Many key parameters improved the thermal boundary layer and temperature. The concentration is low when the chemical reaction parameter and Schmidt number rises. Furthermore, as the bioconvection constant, Peclet and Lewis numbers rise, so does the density of motile microorganisms. [ABSTRACT FROM AUTHOR]

The analysis explored a numerical simulation of microorganisms, carbon nanotubes (CNTs) and ferric oxide water-based hybrid nanofluid flow induced by a wavy fluctuating spinning disc with energy propagation. In the presence of CNTs and magnetic nanoparticulates, the nanofluid is synthesized. The exceptional tensile strength, flexibility, and electrical and thermal conductivity of carbon nanotubes and iron nanoparticles have been extensively reported. The motive of the proposed analysis is to optimize thermal energy conveyance efficiency for a spectrum of industrial and biomedical applications. The phenomena have been expressed as a system of partial differential equations (PDEs) which contain the momentum, energy, concentration, and motile microorganism equations. The modeled equations have been diminished to the dimensionless system of nonlinear ODEs through a similarity framework. The Matlab built-in package boundary value solver has been utilized to solve the obtained system of ODEs. The findings are compared to the PCM technique for validity purposes. The results are illustrated graphically and discussed. The layout of a rotating disc has a positive effect on energy transition and velocity profile. The irregular rotating surface increases energy progression up to 15% relative to a smooth surface. The accumulation of nanocomposites (CNTs and magnetic nanoparticles) significantly enhanced the thermal capabilities of the liquid medium. When operating with a low distribution, it is more impactful. [ABSTRACT FROM AUTHOR]

The study of fluid flow upon an exponentially stretching surface has significant importance due to its applications in technological phenomena at the industrial level. These applications include condensing process of fluid film, heat exchanger processes, extrusion of plastic sheet in aerodynamics, cooling process of metal sheet, and growth of crystals, etc. Keeping in view all these applications, in this paper, we have discussed the magnetohydrodynamic flow of Maxwell fluid past an exponentially stretching sheet. The stretching surface is considered to be slippery by imposing the velocity slip condition. The magnetic field impact is taken into consideration. Furthermore, heat radiation, Joule heating, Brownian motion, and thermophoresis are also considered. The modeled system is reduced to ordinary differential equations with the help of similarity variables. For the analytical solution, we have used the homotopy analysis method. Furthermore, HAM is compared with the shooting method and found to be in great agreement. The squared residual error of the fluid flow problem at 15th order of approximations for Newtonian and non-Newtonian cases has been investigated. It is found that the fluid flow problem converges quickly for the case of non-Newtonian fluid as compared to Newtonian fluid. In addition, the velocity profile increases while the thermal and concentration profiles reduce with greater values of Darcy number. The thermal profile is the increasing function of the Brownian motion parameter and Eckert number whereas the concentration profile is the reducing function of the Brownian motion parameter and Eckert number. With the augmentation in Darcy number, the permeability strength of porous medium increases which concludes the increasing conduct of thermal and mass transportation. [ABSTRACT FROM AUTHOR]

In this modern era, nanofluids are considered one of the advanced kinds of heat transferring fluids due to their enhanced thermal features. The present study is conducted to investigate that how the suspension of molybdenum-disulfide (M o S 2) nanoparticles boosts the thermal performance of a Casson-type fluid. Sodium alginate (NaAlg) based nanofluid is contained inside a vertical channel of width d and it exhibits a flow due to the movement of the left wall. The walls are nested in a permeable medium, and a uniform magnetic field and radiation flux are also involved in determining flow patterns and thermal behavior of the nanofluid. Depending on velocity boundary conditions, the flow phenomenon is examined for three different situations. To evaluate the influence of shape factor, M o S 2 nanoparticles of blade, cylinder, platelet, and brick shapes are considered. The mathematical modeling is performed in the form of non-integer order operators, and a double fractional analysis is carried out by separately solving Caputo-Fabrizio and Atangana-Baleanu operators based fractional models. The system of coupled PDEs is converted to ODEs by operating the Laplace transformation, and Zakian's algorithm is applied to approximate the Laplace inversion numerically. The solutions of flow and energy equations are presented in terms of graphical illustrations and tables to discuss important physical aspects of the observed problem. Moreover, a detailed inspection on shear stress and Nusselt number is carried out to get a deep insight into skin friction and heat transfer mechanisms. It is analyzed that the suspension of M o S 2 nanoparticles leads to ameliorating the heat transfer rate up to 9.5%. To serve the purpose of achieving maximum heat transfer rate and reduced skin friction, the Atangana-Baleanu operator based fractional model is more effective. Furthermore, it is perceived that velocity and energy functions of the nanofluid exhibit significant variations because of the different shapes of nanoparticles. [ABSTRACT FROM AUTHOR]

The magnetic dipole effect for thixotropic nanofluid with heat and mass transfer, as well as microorganism concentration past a curved stretching surface, is discussed. The flow is in a porous medium, which describes the Darcy–Forchheimer model. Through similarity transformations, the governing equations of the problem are transformed into non-linear ordinary differential equations, which are then processed using an efficient and powerful method known as the homotopy analysis method. All the embedded parameters are considered when analyzing the problem through solution. The dipole and porosity effects reduce the velocity, while the thixotropic nanofluid parameter increases the velocity. Through the dipole and radiation effects, the temperature is enhanced. The nanoparticles concentration increases as the Biot number and curvature, solutal, chemical reaction parameters increase, while it decreases with increasing Schmidt number. The microorganism motile density decreases as the Peclet and Lewis numbers increase. Streamlines demonstrate that the trapping on the curved stretched surface is uniform. [ABSTRACT FROM AUTHOR]

Due to the importance of wall shear stress effect and dust fluid in daily life fluid problems. This paper aims to discover the influence of wall shear stress on dust fluids of fluctuating flow. The flow is considered between two parallel plates that are non-conducting. Due to the transformation of heat, the fluid flow is generated. We consider every dust particle having spherical uniformly disperse in the base fluid. The perturb solution is obtained by applying the Poincare-Lighthill perturbation technique (PLPT). The fluid velocity and shear stress are discussed for the different parameters like Grashof number, magnetic parameter, radiation parameter, and dusty fluid parameter. Graphical results for fluid and dust particles are plotted through Mathcad-15. The behavior of base fluid and dusty fluid is matching for different embedded parameters. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks CD 4 + T-cells, which fight against infections and make a person susceptible to other diseases. It is a global public health problem with no cure; therefore, it is highly important to study and understand the intricate phenomena of HIV. In this article, we focus on the numerical study of the path-tracking damped oscillatory behavior of a model for the HIV infection of CD 4 + T-cells. We formulate fractional dynamics of HIV with a source term for the supply of new CD4+ T-cells depending on the viral load via the Caputo–Fabrizio derivative. In the formulation of fractional HIV dynamics, we replaced the constant source term for the supply of new CD 4 + T-cells from the thymus with a variable source term depending on the concentration of the viral load, and introduced a term that describes the incidence of the HIV infection of CD 4 + T-cells. We present a novel numerical scheme for fractional view analysis of the proposed model to highlight the solution pathway of HIV. We inspect the periodic and chaotic behavior of HIV for the given values of input factors using numerical simulations. [ABSTRACT FROM AUTHOR]

To achieve considerably high thermal conductivity, hybrid nanofluids are some of the best alternatives that can be considered as renewable energy resources and as replacements for the traditional ways of heat transfer through fluids. The subject of the present work is to probe the heat and mass transfer flow of an ethylene glycol based hybrid nanofluid (Au-ZnO/C 2 H 6 O 2 ) in three dimensions with homogeneous-heterogeneous chemical reactions and the nanoparticle shape factor. The applications of appropriate similarity transformations are done to make the corresponding non-dimensional equations, which are used in the analytic computation through the homotopy analysis method (HAM). Graphical representations are shown for the behaviors of the parameters and profiles. The hybrid nanofluid (Au-ZnO/C 2 H 6 O 2 ) has a great influence on the flow, temperature, and cubic autocatalysis chemical reactions. The axial velocity and the heat transfer increase and the concentration of the cubic autocatalytic chemical reactions decreases with increasing stretching parameters. The tangential velocity and the concentration of cubic autocatalytic chemical reactions decrease and the heat transfer increases with increasing Reynolds number. A close agreement of the present work with the published study is achieved. [ABSTRACT FROM AUTHOR]

In this article, we propose a localized transform based meshless method for approximating the solution of the 2D multi-term partial integro-differential equation involving the time fractional derivative in Caputo's sense with a weakly singular kernel. The purpose of coupling the localized meshless method with the Laplace transform is to avoid the time stepping procedure by eliminating the time variable. Then, we utilize the local meshless method for spatial discretization. The solution of the original problem is obtained as a contour integral in the complex plane. In the literature, numerous contours are available; in our work, we will use the recently introduced improved Talbot contour. We approximate the contour integral using the midpoint rule. The bounds of stability for the differentiation matrix of the scheme are derived, and the convergence is discussed. The accuracy, efficiency, and stability of the scheme are validated by numerical experiments. [ABSTRACT FROM AUTHOR]

This paper focuses on advances in the understanding of both the fundamental and applied aspects of nanomaterials. Nanoparticles (titania and graphene oxide) in water-based fluid lying on a surface incorporating the leading edge accretion (or ablation) are analyzed. Entropy generation rate is also considered. The Hall current effect is induced in the flow of hybrid nanofluid, due to which the two-dimensional study converts into three-dimensional space. Similarity transformations convert the equations of momentum, heat transfer, nanoparticles volume fraction and boundary conditions into non-dimensional form. Mathematica software is used to obtain the computation through homotopy analysis method. Analysis is provided through the effects of different parameters on different profiles by sketching the graphs. Flow, heat transfer and nanoparticles concentration in TiO 2 /H 2 O, as well as GO-TiO 2 /H 2 O, are decreased with increasing the Stefan blowing effect, while entropy generation rate elevates upon increasing each parameter. Both of the velocity components are reduced with increasing the Hall parameter. Streamlines demonstrate that trapping is increased at the left side of the surface. The obtained results are compared with the published work which show the authentication of the present work. [ABSTRACT FROM AUTHOR]

In this article, we propose a new modified extragradient-like method to solve pseudomonotone equilibrium problems in real Hilbert space with a Lipschitz-type condition on a bifunction. This method uses a variable stepsize formula that is updated at each iteration based on the previous iterations. The advantage of the method is that it operates without prior knowledge of Lipschitz-type constants and any line search method. The weak convergence of the method is established by taking mild conditions on a bifunction. In the context of an application, fixed-point theorems involving strict pseudo-contraction and results for pseudomonotone variational inequalities are considered. Many numerical results have been reported to explain the numerical behavior of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a real Hilbert space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration based on some previous iterations. The key advantage of the algorithm is that it is achieved without previous knowledge of the Lipschitz-type constants and also without any line search procedure. A weak convergence theorem for the proposed method is well established by assuming mild cost bifunction conditions. Many numerical experiments are presented to explain the computational performance of the method and to equate them with others. [ABSTRACT FROM AUTHOR]

This manuscript aims to incorporate an inertial scheme with Popov's subgradient extragradient method to solve equilibrium problems that involve two different classes of bifunction. The novelty of our paper is that methods can also be used to solve problems in many fields, such as economics, mathematical finance, image reconstruction, transport, elasticity, networking, and optimization. We have established a weak convergence result based on the assumption of the pseudomonotone property and a certain Lipschitz-type cost bifunctional condition. The stepsize, in this case, depends upon on the Lipschitz-type constants and the extrapolation factor. The bifunction is strongly pseudomonotone in the second method, but stepsize does not depend on the strongly pseudomonotone and Lipschitz-type constants. In contrast, the first convergence result, we set up strong convergence with the use of a variable stepsize sequence, which is decreasing and non-summable. As the application, the variational inequality problems that involve pseudomonotone and strongly pseudomonotone operator are considered. Finally, two well-known Nash–Cournot equilibrium models for the numerical experiment are reviewed to examine our convergence results and show the competitive advantage of our suggested methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Euclidean, Hamming, and generalized distance measures for the generalized intuitionistic fuzzy soft sets (GIFSSs). We discuss the properties of the presented distance measures. The numerical example of decision making and pattern recognition is discussed based on the proposed distance measures. We develop a remoteness index-based VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for GIFSSs. The displaced and fixed ideals intuitionistic fuzzy values (IFVs) are defined. The novel concept of displaced and fixed remoteness indexes for IFVs are discussed. We discuss the methods to obtain the precise and intuitionistic fuzzy (IF) weights. The several displaced and fixed ranking indexes are defined based on the precise and IF weights. The remoteness indexes based VIKOR methods are proposed in the form of four algorithms. In the end, the selection of renewable energy sources problem is solved by using the four remoteness index-based VIKOR methods. [ABSTRACT FROM AUTHOR]

The flow of conducting Carreau fluid on a permeable stretching/shrinking surface is analytically investigated by considering the thermal radiation, mass transfer, and cross diffusion effects. A uniform external magnetic field is employed which gives rise to Hall current. The nonlinear PDEs are converted to a set of ODEs using similarity transformations. The developed ODEs are solved using the well established mathematical procedure of Homotopy Analysis Method (HAM). The influence of associated parameters over the state variables of the Carreau fluid are analytically studied and discussed through different graphs. It is found that fluid velocity augments (drops) with the rising power law index and Hall parameter (velocity slip and material parameters). The temperature field increases with the higher Dufour number and radiation parameter values, and decreases with larger Prandtl number. The concentration field augments with the larger Soret number and velocity slip parameter values whereas drops with the rising Schmidt number. The variations in skin friction, local Nusselt and Sherwood numbers are discussed using tables and it is noticed that the mass and heat energy transfer rates are controlled by the varying values of Dufour and Soret parameters. The comparison between present and published work shows complete agreement. [ABSTRACT FROM AUTHOR]

This article is focused on an original control approach applied to a transportation system that includes a polymer electrolyte membrane fuel cell (PEMFC) as the main energy source and supercapacitors (SC) as the energy storage backup. To interface the SC with the DC bus of the embedded network, a two-port bidirectional DC-DC converter was used. To control the system and ensure its stability, a reduced-order mathematical model of the network was developed through a nonlinear control approach employing a differential flatness algorithm, which is an attractive and efficient solution to make the system stable by overcoming the dynamic issues generally met in the power electronics networks of transportation systems. The design and tuning of the system control were not linked with the equilibrium point at which the interactions between the PEMFC main source, the SC energy storage device, and the loads are taken into consideration by the proposed control law. Besides this, high dynamics in the load power rejection were accomplished, which is the main contribution of this article. To verify the effectiveness of the developed control law, a small-scale experimental test rig was realized in the laboratory and the control laws were implemented in a dSPACE 1103 controller board. The experimental tests were performed with a 1 kW PEMFC source and a 250 F 32 V SC module as an energy storage backup. Lastly, the performances of the proposed control strategy were validated based on real experimental results measured during driving cycles, including motoring mode, ride-though, and regenerative braking mode. [ABSTRACT FROM AUTHOR]

In this work, a pair of embedded explicit exponentially-fitted Runge–Kutta–Nyström methods is formulated for solving special second-order ordinary differential equations (ODEs) with periodic solutions. A variable step-size technique is used for the derivation of the 5(3) embedded pair, which provides a cheap local error estimation. The numerical results obtained signify that the new adapted method is more efficient and accurate compared with the existing methods. [ABSTRACT FROM AUTHOR]

In this work, we introduce an efficient scheme for the numerical solution of some Boundary and Initial Value Problems (BVPs-IVPs). By using an operational matrix, which was obtained from the first kind of Chebyshev polynomials, we construct the algebraic equivalent representation of the problem. We will show that this representation of BVPs and IVPs can be represented by a sparse matrix with sufficient precision. Sparse matrices that store data containing a large number of zero-valued elements have several advantages, such as saving a significant amount of memory and speeding up the processing of that data. In addition, we provide the convergence analysis and the error estimation of the suggested scheme. Finally, some numerical results are utilized to demonstrate the validity and applicability of the proposed technique, and also the presented algorithm is applied to solve an engineering problem which is used in a beam on elastic foundation. [ABSTRACT FROM AUTHOR]

In this paper, we propose a two-step iterative algorithm based on projection technique for solving system of monotone nonlinear equations with convex constraints. The proposed two-step algorithm uses two search directions which are defined using the well-known Barzilai and Borwein (BB) spectral parameters.The BB spectral parameters can be viewed as the approximations of Jacobians with scalar multiple of identity matrices. If the Jacobians are close to symmetric matrices with clustered eigenvalues then the BB parameters are expected to behave nicely. We present a new line search technique for generating the separating hyperplane projection step of Solodov and Svaiter (1998) that generalizes the one used in most of the existing literature. We establish the convergence result of the algorithm under some suitable assumptions. Preliminary numerical experiments demonstrate the efficiency and computational advantage of the algorithm over some existing algorithms designed for solving similar problems. Finally, we apply the proposed algorithm to solve image deblurring problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider an order-preserving mapping T on a complete partial b-metric space satisfying some contractive condition. We were able to show the existence and uniqueness of the fixed point of T. In the application aspect, the fidelity of quantum states was used to establish the existence of a fixed quantum state associated to an order-preserving quantum operation. The method we presented is an alternative in showing the existence of a fixed quantum state associated to quantum operations. Our method does not capitalise on the commutativity of the quantum effects with the fixed quantum state(s) (Luders's compatibility criteria). The Luders's compatibility criteria in higher finite dimensional spaces is rather difficult to check for any prospective fixed quantum state. Some part of our results cover the famous contractive fixed point results of Banach, Kannan and Chatterjea. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to establish new oscillation results of solutions to a class of even-order advanced differential equations with a p-Laplacian like operator. The key idea of our approach is to use the Riccati transformation and the theory of comparison with first and second-order delay equations. Some examples are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we propose two modified two-step proximal methods that are formed through the proximal-like mapping and inertial effect for solving two classes of equilibrium problems. A weak convergence theorem for the first method and the strong convergence result of the second method are well established based on the mild condition on a bifunction. Such methods have the advantage of not involving any line search procedure or any knowledge of the Lipschitz-type constants of the bifunction. One practical reason is that the stepsize involving in these methods is updated based on some previous iterations or uses a stepsize sequence that is non-summable. We consider the well-known Nash–Cournot equilibrium models to support our well-established convergence results and see the advantage of the proposed methods over other well-known methods. [ABSTRACT FROM AUTHOR]

The relaxed inertial Tseng-type method for solving the inclusion problem involving a maximally monotone mapping and a monotone mapping is proposed in this article. The study modifies the Tseng forward-backward forward splitting method by using both the relaxation parameter, as well as the inertial extrapolation step. The proposed method follows from time explicit discretization of a dynamical system. A weak convergence of the iterates generated by the method involving monotone operators is given. Moreover, the iterative scheme uses a variable step size, which does not depend on the Lipschitz constant of the underlying operator given by a simple updating rule. Furthermore, the proposed algorithm is modified and used to derive a scheme for solving a split feasibility problem. The proposed schemes are used in solving the image deblurring problem to illustrate the applicability of the proposed methods in comparison with the existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The object of this study was to demonstrate the ability of machine learning (ML) methods for the segmentation and classification of diabetic retinopathy (DR). Two-dimensional (2D) retinal fundus (RF) images were used. The datasets of DR—that is, the mild, moderate, non-proliferative, proliferative, and normal human eye ones—were acquired from 500 patients at Bahawal Victoria Hospital (BVH), Bahawalpur, Pakistan. Five hundred RF datasets (sized 256 × 256) for each DR stage and a total of 2500 (500 × 5) datasets of the five DR stages were acquired. This research introduces the novel clustering-based automated region growing framework. For texture analysis, four types of features—histogram (H), wavelet (W), co-occurrence matrix (COM) and run-length matrix (RLM)—were extracted, and various ML classifiers were employed, achieving 77.67%, 80%, 89.87%, and 96.33% classification accuracies, respectively. To improve classification accuracy, a fused hybrid-feature dataset was generated by applying the data fusion approach. From each image, 245 pieces of hybrid feature data (H, W, COM, and RLM) were observed, while 13 optimized features were selected after applying four different feature selection techniques, namely Fisher, correlation-based feature selection, mutual information, and probability of error plus average correlation. Five ML classifiers named sequential minimal optimization (SMO), logistic (Lg), multi-layer perceptron (MLP), logistic model tree (LMT), and simple logistic (SLg) were deployed on selected optimized features (using 10-fold cross-validation), and they showed considerably high classification accuracies of 98.53%, 99%, 99.66%, 99.73%, and 99.73%, respectively. [ABSTRACT FROM AUTHOR]

This article analyzes heat transfer enhancement in incompressible time dependent magnetohydrodynamic (MHD) convective flow of Oldroyd-B nanofluid with carbon nanotubes (CNTs). Single wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) are immersed in a base fluid named Sodium alginate. The flow is restricted to an infinite vertical plate saturated in a porous material incorporating the generalized Darcy's law and heat suction/injection. The governing equations for momentum, shear stress and energy are modelled in the form of partial differential equations along with ramped wall temperature and ramped wall velocity boundary conditions. Laplace transformation is applied to convert principal partial differential equations to ordinary differential equations first and, later, complex multivalued functions of Laplace parameter are handled with numerical inversion to obtain the solutions in real time domain. Expression for Nusselt number is also obtained to clearly examine the difference in rate of heat transfer. A comparison for isothermal wall condition and ramped wall condition is also made to analyze the difference in both profiles. A graphical study is conducted to analyze how the fluid profiles are significantly affected by several pertinent parameters. Rate of heat transfer increases with increasing volume fraction of nanoparticle while shear stress reduces with elevation in retardation time. Moreover, flow gets accelerated with increase in Grashof number and Porosity parameter. For every parameter, a comparison between solutions of SWCNTs and MWCNTs is also presented. [ABSTRACT FROM AUTHOR]

In this work, we study the oscillatory behavior of a class of fourth-order differential equations. New oscillation criteria were obtained by employing a refinement of the Riccati transformations. The new theorems complement and improve a number of results reported in the literature. An example is provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

The main objective of this article is to propose a new method that would extend Popov's extragradient method by changing two natural projections with two convex optimization problems. We also show the weak convergence of our designed method by taking mild assumptions on a cost bifunction. The method is evaluating only one value of the bifunction per iteration and it is uses an explicit formula for identifying the appropriate stepsize parameter for each iteration. The variable stepsize is going to be effective for enhancing iterative algorithm performance. The variable stepsize is updating for each iteration based on the previous iterations. After numerical examples, we conclude that the effect of the inertial term and variable stepsize has a significant improvement over the processing time and number of iterations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method, which is set up by incorporating an inertial step with the extragradient method for solving a strongly pseudomonotone equilibrium problems. This method had to comply with a strongly pseudomonotone property and a certain Lipschitz-type condition of a bifunction. A strong convergence result is provided under some mild conditions, and an iterative sequence is accomplished without previous knowledge of the Lipschitz-type constants of a cost bifunction. A sufficient explanation is that the method operates with a slow-moving stepsize sequence that converges to zero and non-summable. For numerical explanations, we analyze a well-known equilibrium model to support our well-established convergence result, and we can see that the proposed method seems to have a significant consistent improvement over the performance of the existing methods. [ABSTRACT FROM AUTHOR]

Two inertial subgradient extragradient algorithms for solving variational inequality problems involving pseudomonotone operator are proposed in this article. The iterative schemes use self-adaptive step sizes which do not require the prior knowledge of the Lipschitz constant of the underlying operator. Furthermore, under mild assumptions, we show the weak and strong convergence of the sequences generated by the proposed algorithms. The strong convergence in the second algorithm follows from the use of viscosity method. Numerical experiments both in finite- and infinite-dimensional spaces are reported to illustrate the inertial effect and the computational performance of the proposed algorithms in comparison with the existing state of the art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose, analyze, and test an alternative method for solving the ℓ 1 -norm regularization problem for recovering sparse signals and blurred images in compressive sensing. The method is motivated by the recent proposed nonlinear conjugate gradient method of Tang, Li and Cui [Journal of Inequalities and Applications, 2020(1), 27] designed based on the least-squares technique. The proposed method aims to minimize a non-smooth minimization problem consisting of a least-squares data fitting term and an ℓ 1 -norm regularization term. The search directions generated by the proposed method are descent directions. In addition, under the monotonicity and Lipschitz continuity assumption, we establish the global convergence of the method. Preliminary numerical results are reported to show the efficiency of the proposed method in practical computation. [ABSTRACT FROM AUTHOR]

A new condition on positive membership, neutral membership, and negative membership functions give us the successful extension of picture fuzzy set and Pythagorean fuzzy set and called spherical fuzzy sets (SFS) . This extends the domain of positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measure and application in data mining, medical diagnosis, decision making, and pattern recognition, several studies on similarity measures have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we proposed the set-theoretic similarity and distance measures. We provide some counterexamples for already proposed similarity measures in the literature and shows that how our proposed method is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for selecting mega projects in under developed countries. [ABSTRACT FROM AUTHOR]

In this article, we focus on improving the sub-gradient extra-gradient method to find a solution to the problems of pseudo-monotone equilibrium in a real Hilbert space. The weak convergence of our method is well-established based on the standard assumptions on a bifunction. We also present the application of our results that enable to solve numerically the pseudo-monotone and monotone variational inequality problems, in addition to the particular presumptions required by the operator. We have used various numerical examples to support our well-proved convergence results, and we can show that the proposed method involves a considerable influence over-running time and the total number of iterations. [ABSTRACT FROM AUTHOR]

This article provides a comprehensive analysis regarding effects of ramped wall temperature and ramped wall velocity on incompressible time-dependent magnetohydrodynamic flow of Maxwell fluid. The flow is due to free convection and bounded to an infinite vertical plate embedded in porous medium. Solutions of mass, shear stress, and energy fields are computed symmetrically by introducing some suitable non-dimensional parameters along with the Laplace transformation technique. The expression for the Nusselt number is also calculated. A comparison between solutions incorporating isothermal temperature and ramped wall temperature conditions is also executed to examine the profile differences. A graphical study is performed to highlight the influence of parameters on mass flow and energy transfer. [ABSTRACT FROM AUTHOR]

The objective of this study is to highlight the stress factors influencing primary school female teachers in southern Punjab, Pakistan. A causation model is developed to determine the effect of the three main domains of stress. Data were collected through a questionnaire using a convenient sampling technique. Cronbach's alpha is computed to determine the internal consistency of the items of the questionnaire. The factors involved in the causation model are confirmed through confirmatory factor analysis. The perceived stress scale is used to check the stress level in primary school female teachers. A structural pathway of social, health and environmental factors is designed to determine the influence of different variables on stress. The examined problems included the four following major areas: social factors, economic factors, health factors and environment factors. Among our results, it is shown that the marital status has an effect on the stress level of both public and private female school teachers. [ABSTRACT FROM AUTHOR]

In this research article, we investigated a comprehensive analysis of time-dependent free convection electrically and thermally conducted water-based nanofluid flow containing Copper and Titanium oxide (Cu and TiO 2 ) past a moving porous vertical plate. A uniform transverse magnetic field is imposed perpendicular to the flow direction. Thermal radiation and heat sink terms are included in the energy equation. The governing equations of this flow consist of partial differential equations along with some initial and boundary conditions. The solution method of these flow interpreting equations comprised of two parts. Firstly, principal equations of flow are symmetrically transformed to a set of nonlinear coupled dimensionless partial differential equations using convenient dimensionless parameters. Secondly, the Laplace transformation technique is applied to those non-dimensional equations to get the close form exact solutions. The control of momentum and heat profile with respect to different associated parameters is analyzed thoroughly with the help of graphs. Fluid accelerates with increasing Grashof number (Gr) and porosity parameter (K), while increasing values of heat sink parameter (Q) and Prandtl number (Pr) drop the thermal profile. Moreover, velocity and thermal profile comparison for Cu and TiO 2 -based nanofluids is graphed. [ABSTRACT FROM AUTHOR]

Present theoretical investigation is a mathematical illustration of an application to endoscopy by incorporating hybrid nanoparticles and an induced magnetic field with a rheological fluid model for more realistic results. Rheological fluid behavior is characterized by the Ostwald-de-Waele power-law model. A hybrid nanofluid mechanism is considered comprising platelet-shaped nanoparticles since nanoparticles are potential drug transportation tools in biomedical applications. Moreover, ciliary activity is encountered regarding their extensive applications in performing complex functions along with buoyancy effects. An endoscope is inserted inside a ciliated tube and peristalsis occurred due to ciliary activity in the gap between tube and endoscope. A non-Newtonian model is developed by mathematical formulation which is tackled analytically using homotopy analysis. The outcomes are interpreted graphically along with the pressure rise and streamlining configuration for the case of negligible inertial forces and long wavelength. A three-dimensional graphical interpretation of axial velocity is studied as well. Moreover, tables are prepared and displayed for a more physical insight. [ABSTRACT FROM AUTHOR]

This paper examines the time independent and incompressible flow of magnetohydrodynamic (MHD) nanofluid through a porous rotating disc with velocity slip conditions. The mass and heat transmission with viscous dissipation is scrutinized. The proposed partial differential equations (PDEs) are converted to ordinary differential equation (ODEs) by mean of similarity variables. Analytical and numerical approaches are applied to examine the modeled problem and compared each other, which verify the validation of both approaches. The variation in the nanofluid flow due to physical parameters is revealed through graphs. It is witnessed that the fluid velocities decrease with the escalation in magnetic, velocity slip, and porosity parameters. The fluid temperature escalates with heightening in the Prandtl number, while other parameters have opposite impacts. The fluid concentration augments with the intensification in the thermophoresis parameter. The validity of the proposed model is presented through Tables. [ABSTRACT FROM AUTHOR]

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer's and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results. [ABSTRACT FROM AUTHOR]

This article analyzes the time-dependent magnetohydrodynamic flow of Oldroyed-B fluid in the presence of heat consumption/generation and thermal radiation. The flow is restricted to a vertical infinite plate saturated in porous material along with ramp wall velocity and ramp wall temperature conditions. This flow also incorporates the generalized Darcy's law. In this paper, accurate equation of velocity field is presented first and then solutions of mass and energy equation are derived in Laplace domain. Real-time domain solutions are obtained by tackling the complexity of Laplace domain expressions through numerical Laplace inversion. Skin friction coefficient and Nusselt number are also calculated. A comparison for ramp wall temperature condition and isothermal temperature condition is also drawn to investigate the difference. A graphical study is conducted to analyze the influence of parameters on fluid flow and heat transfer. It is found that radiation parameter and heat generation elevate the energy profile, while flow is accelerated by increasing the retardation time and porosity parameter and an opposite behavior is noted for increasing relaxation time and magnetic parameter. Furthermore, heat transfer rate is higher for increasing Prandtl number and velocity on plate decreases with increase in relaxation time λ 1 . [ABSTRACT FROM AUTHOR]

In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L 2 and L ∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before. [ABSTRACT FROM AUTHOR]