The investigation detailed in this paper explores the behavior of a slippery nanofluid flowing over permeable stretched sheet under influence magnetohydrodynamic forces, considering factors like thermal radiation, viscous dissipation, and convective boundary conditions. analysis systematically establishes principles for conserving mass, heat, momentum, nanoparticle concentration, deriving set nonlinear ordinary differential equations from governing partial equations. To tackle these...

We provide an effective simulation to investigate the solution behavior of nine-dimensional chaos for fractional (Caputo-sense) Lorenz system using a new approximate technique spectral collocation method (SCM) depending on properties Gegenbauer wavelet polynomials (GWPs). This reduces given problem non-linear algebraic equations. satisfy accuracy and efficiency proposed by computing residual error function. The numerical solutions obtained are compared with results implementing Runge–Kutta...

A numerical method for solving the fractional‐order logistic differential equation with two different delays (FOLE) is considered. The fractional derivative described in Caputo sense. proposed based upon Chebyshev approximations. properties of polynomials are utilized to reduce FOLE a system algebraic equations. Special attention given study convergence and error estimate presented method. Numerical illustrations demonstrate utility Chaotic behavior observed smallest order chaotic obtained....

This paper presents an accurate numerical method for solving fractional Riccati differential equation (FRDE). The proposed so called Chebyshev finite difference (FCheb-FDM). In this technique, we approximate FRDE with a dimensional problem. is based on the combination of useful properties polynomials approximation and method. Caputo derivative replaced by quotient integral sum. By given problem reduced to system algebraic equations, system, obtain solution FRDE. Special attention study...

This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated by optimization problem using Chebyshev collocation method.The derivatives presented in terms Caputo sense.The application proposed method to FDEs leads algebraic can be solved Newton iteration introduces a promising tool for solving many systems non-linear FDEs.Two examples provided confirm accuracy and effectiveness methods.Comparisons finite difference (FDM) fourth...

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use spectral collocation which based upon Chebyshev approximations. The properties of polynomials third kind are used to reduce proposed problem a system ODEs, solved by finite difference (FDM). Some theorems about convergence analysis stated and proved. A simulation given results compared with exact solution.

We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such are presented as nonlinear differential—difference equations. The proposed method is based on Laplace transform with homotopy analysis (HAM). This powerful tool large amount of problems. technique provides series functions which may converge to exact solution problem. A good agreement between obtained and some well-known results obtained.

This paper is devoted to introduce a numerical simulation using finite difference method with the theoretical study for problem of flow and heat transfer over an unsteady stretching sheet embedded in porous medium presence thermal radiation. The continuity, momentum energy equations, which are coupled nonlinear partial differential equations reduced set two ordinary before being solved numerically implicit, iterative (FDM). accuracy proposed tested by performing various comparisons...

In this paper, the explicit finite difference method (FDM) is used to study variable order nonlinear fractional wave equation. The derivative described in Riesz sense. Special attention given stability analysis and convergence of proposed method. Numerical test examples are presented show efficiency numerical scheme.

In this study, we propose to introduce and apply an accurate numerical procedure solve the mathematical model of fractional order, which describes electrical circuits composed resistors inductors (RL) driven by a voltage current source. Our research is based on spectral collocation method, utilizes advantageous characteristics third‐order Chebyshev polynomials. Some convergence analysis error theorems are presented. The proposed concludes comparing approximate solutions obtained for...

Smoking is a social trend that prevalent around the world, particularly in places of learning and at some significant events. The World Health Organization (WHO) defines smoking as most important preventable cause disease third major death humans. So, this paper, we present an effective simulation to study solution behavior Liouville-Caputo fractional-order model by using presumably new approximation technique based on Gegenbauer wavelet polynomials (GWPs). We use spectral collocation method...

Some researchers have started to perform in-depth studies on carbon dioxide emissions phenomena because global warming has caused immense damage. In this work, as a generalization of these studies, we will investigate and describe the fractional delayed Carbon absorption-emission model which consists two (Caputo sense) differential equations. From point, study behavior solution for by using an approximate technique based Appell-type Changhee polynomials (ACPs). We present approximation...

In this article, a numerical study for the fractional wave equations is introduced by using class of finite difference methods.These methods are extension weighted average ordinary (non-fractional) equations.The stability analysis proposed given recently procedure similar to standard John von Neumann analysis.Simple and accurate criterion valid different discretization schemes derivative, arbitrary weight factor, order checked numerically.Numerical test example comparisons have been...

In this article, a numerical study is introduced for solving the fractional wave equations by using an efficient class of finite difference methods. The proposed scheme based on Hermite formula. stability and convergence analysis methods are given recently procedure similar to standard von Neumann analysis. A simple accurate criterion valid different discretization schemes derivative, arbitrary weight factor, order checked numerically. Finally, example presented confirm theoretical results.

The current work examines the transfer of heat/mass in a thin liquid film (TLF) with high viscosity on surface that is continuously stretching. Through thorough mathematical modeling, system PDEs established. application appropriate similarity transformations results formulation set nonlinear ODEs from original PDEs. Here, we introduce reliable numerical technique to analyze solution characteristics proposed problem. This depends applying shifted Chebyshev polynomials sixth-order (SCP6s)....