in this work, we have applied elzaki transform and he's homotopy perturbation method to solvepartial dierential equation (pdes) with time-fractional derivative. with help he's homotopy per-turbation, we can handle the nonlinear terms. further, we have applied this suggested he's homotopyperturbation method in order to reformulate initial value problem. some illustrative examples...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to il...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

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...

Abstract In this article we propose a hybrid method based on local meshless and the Laplace transform for approximating solution of linear one dimensional partial differential equations in sense Caputo–Fabrizio fractional derivative. our numerical scheme is used to avoid time stepping procedure, produce sparse differentiation matrices ill conditioning issues resulting global methods. Our compri...

‎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...