The main goal of this work is to find the solutions linear and nonlinear fractional differential equations with Mittag-Leffler nonsingular kernel. An accurate numerical method search problem has been constructed. theoretical results are proved by utilizing two experiments.

Abstract The current analysis signifies the Casson nanofluid stream with inclined magnetohydrodynamics, viscous dissipation, joule heating, thermal radiation, particle shape factor effects over a moving flat horizontal surface entropy analysis. This study presents novel idea regarding implementation of Tiwari and Das model on fluid by considering ethylene glycol as base fluid. considers nanoparticles volume fraction for heat transfer enhancement instead Buongiorno which heavily relies...

The objective of the present article is to investigate an incompressible micropolar Prandtl fluid flowing over a porous stretching sheet with inclusion effects like exponential temperature-dependent heat source, higher-order chemical reaction viscous dissipation, nonlinear thermal radiation, and multiple convective surface boundary conditions. partial differential equations (PDEs) for momentum, energy, micro-rotation, concentration are discussed. These PDEs converted into ordinary (ODEs) by...

In this article, we propose the integrator circuit model by fractal-fractional operator in which fractional-order has taken Atangana-Baleanu sense. Through Schauder's fixed point theorem, establish existence theory to ensure that posses at least one solution and via Banach guarantee proposed a unique solution. We derive results for Ulam-Hyres stability mean of non-linear functional analysis shows is stable under new derivative. numerical consideration through Atanaga-Toufik method. simulate...

<abstract><p>In this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence uniqueness of solutions for proposed fractional are obtained. basic reproduction number, equilibrium points, stability analysis derived. Sensitivity carried out to elaborate influential parameters upon number. It obtained that disease transmission parameter most dominant A convergent iterative scheme taken into...

In this paper, we find the solutions of fourth order fractional boundary value problems by using reproducing kernel Hilbert space method. Firstly, method is introduced and then applied to kind problems. The experiments are discussed approximate obtained be more correct compared other results in literature.

In this study, we solved the economic models based on market equilibrium with constant proportional Caputo derivative using Laplace transform. We proved accuracy and efficiency of method. constructed relations between solutions problems bivariate Mittag–Leffler functions.

Numerical methods play an important role in modern mathematical research, especially studying the symmetry analysis and obtaining numerical solutions of fractional differential equation. In current work, we use two schemes to deal with equations. first case, a combination group preserving scheme fictitious time integration method (FTIM) is considered solve problem. Firstly, applied FTIM role, then GPS came integrate obtained new system using initial conditions. Figure tables containing are...

Solar power is the primary thermal energy source from sunlight. This research has carried out study of solar aircraft with radiation in enhancing efficiency. The transfer inside wings using a nanofluid past parabolic surface trough collector (PTSC) investigated thoroughly. heat regarded as radiation. For several impacts, such porous medium, radiation, and varying conductivity, transmission performance examined. By tangent hyperbolic (THNF), entropy analysis been performed. modeled momentum...

A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM).The resulting equation with magneto-hydrodynamic flow transformed to the nonlinear system introducing dimensionless variables.Results are presented graphically study efficiency and accuracy of method.Results show that this namely RKM an efficient solving in any engineering field.

Abstract In this article, we investigate the mechanics of breathing performed by a ventilator with different kernels an effective integral transform. We mainly obtain solutions fractional respiratory model. Our goal is to give underlying model flexibly making use advantages non-integer order operators. The big advantage derivatives that can formulate models describing much better systems memory effects. Fractional operators memories are related types relaxation process non-local dynamical...

In 2017, Atangana proposed more generalized operators depending on two parameters: one is fractional order (FO) and other fractal dimension. The novel are defined with three different kernels. These produced excellent dynamics of the chaotic systems. this paper, Caputo fractal-fractional operator used to explore a system which contains only signum function. existence theory developed by using fixed-point result Leray–Schauder prove that considered possesses at least solution. has unique...

This paper outlines a comprehensive study of the fluid-flow in presence heat and mass transfer. The governing non-linear ODE are solved by means homotopy perturbation method. A comparison present solution is also made with existing excellent agreement observed. implementation method proved to be extremely effective highly suitable. procedure explicitly elucidates remarkable accuracy proposed algorithm.

Abstract In this research, we analyze the magnetohydrodynamics heat act of a viscous incompressible Jeffrey nanoliquid, which passed in neighborhood linearly extending foil. As process, employ alumina <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:msub> <m:mi mathvariant="normal">Al</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> mathvariant="normal">O</m:mi> <m:mn>3</m:mn> <m:mo>)</m:mo> </m:math> \left({{\rm{Al}}}_{2}{{\rm{O}}}_{3}) as nanoparticles, assuming...

Abstract The aim of this work is to tackle the three–dimensional (3D) Heston– Cox–Ingersoll–Ross (HCIR) time–dependent partial differential equation (PDE) computationally by employing a non–uniform discretization and gathering finite difference (FD) weighting coe cients into differentiation matrices. In fact, 3D computational domain employed achieve second–order accuracy for all spatial variables. It contributed that under what conditions proposed procedure stable. This stability bound novel...

Abstract Solar energy is about the study of solar radiations and a method to enhance efficacy aircrafts with utilization nanotechnology. has been considered heat source. The transmission performance wings scrutinized for situation various effects like thermal radiations, generation, variant conductance, conductivity, viscidness dissipative flow. Entropy generation analysis carried out in status Reiner Philippoff nanofluid (RPNF). aircraft (SACW) improves relations amplification radiation,...

In the present work, new iterative method with a combination of Laplace transform Caputo's fractional derivative has been applied to generalized (3 + 1) dimensional perturbed Zakharov–Kuznetsov equation in dusty plasma. The proposed is without any discretization and linearization. numerical graphical results show accuracy for nonlinear differential equations. Moreover, methods are easy implement give efficient approximate solutions.

In this paper, we investigate the fractal-fractional Malkus Waterwheel model in detail. We discuss existence and uniqueness of a solution using fixed point technique. apply very effective method to obtain solutions model. prove with numerical simulations accuracy proposed method. put evidence effects fractional order fractal dimension for symmetric

Reproducing kernel Hilbert space method is given for nonlinear boundary‐value problems in this paper. Applying technique, we establish a new algorithm to approximate the solution of such problems. This technique does not need any background mesh and can easily be applied. In form series. Representation solutions obtained reproducing space. Additionally, convergence presented demonstrated. Numerical examples are show ability method. We compare with B‐spline collocation As seen tables, gives...

In this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied get approximate solutions of such We obtain some useful functions solutions. very efficient results by method. show our numerical tables.

In this paper we construct some new reproducing kernel functions in the Sobolev space. These are literature. We can solve many problems by these spaces.