In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...

‎in this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(vofides‎, ‎for short)‎. ‎in these equations‎, ‎the variable-order fractional integration(vofi) and‎ ‎variable-order fractional derivative (vofd) are described in the‎ ‎riemann-liouville's and caputo's sense,respectively‎. ‎numerical experiments‎, ‎consisting of two exam...

The purpose of this study is to develop a new approach in modeling and simulation of a reverse osmosis desalination system by using fractional differential equations. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. Examples are developed to illustrate the fractional differential techniq...

Present paper deals with the solution of time and space fractional Pennes bioheat equation. We consider time fractional derivative and space fractional derivative in the form of Caputo fractional derivative of order [Formula: see text] and Riesz-Feller fractional derivative of order [Formula: see text] respectively. We obtain solution in terms of Fox's H-function with some special cases, by usi...

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

Conformable fractional calculus will be a promising area of research for information processing as natural language and material modelling due to its ease implementation. In this paper, we propose gradient descent method the backpropagation training neural networks. particular, conformable is employed evaluate differential function instead classical function. The results obtained on large datas...

Abstract In the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019), authors have used Krasnoselskii fixed point theorem for showing existence of mild solutions an abstract class conformable fractional differential equations form: $\frac{d^{\alpha }}{dt^{\alpha }}[\frac{d^{\alpha }x(t)}{dt^{\alpha }}]=Ax(t)+f(t,x(t))$ <...