The functional effects of medications, such as those that slow down and calm the body, have been investigated for polarized diffusion coefficient based on subsequent increase through magnetism. This study examines generalized Mittag–Lefer kernel-based fractional derivatives in MHD Brinkman-type fluids under bioconvection contain hybrid titanium dioxide (TiO 2 ) silver (Ag) nanoparticles with wa...

Abstract The goal of this article is to present a recently developed numerical approach for solving fractional stochastic differential equations with singular Caputo kernel and nonsingular Caputo–Fabrizio Atangana–Baleanu (ABC) kernel. proposed method based on the discrete Temimi–Ansari method, which combined three different schemes that are appropriate new derivative operators. technique used ...

In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

The fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for nonlinear fractional dispersive long wave equation with reaspect to time fractional derivative. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the ...

The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classical theory of linear viscoelasticity, we contrast these two types of fractional derivatives in thei...

This article presents the analytical study of three species fractional food web model in framework Modified Caputo–Fabrizio operator. With help fixed point theory, existence and uniqueness results are investigated for order model. To obtain approximate solution suggested model, well-known Laplace–Adomian decomposition method is used. The solutions validated through simulations with a variety or...