SOLVING FRACTIONAL INTEGRO DIFFERENTIAL EQUATIONS BY HOMOTOPY ANALYSIS TRANSFORM METHOD

M.S Mohamed,M.R Alharthi,R.A Alotabi

doi:10.12732/ijpam.v106i4.6

Abstract

In this paper, we introduce an analytical method, which so called the homotopy analysis transform method (HATM) which is a combination of HAM and Laplace decomposition method (LDM). This scheme is simple to apply linear and nonlinear fractional integro-differential equation and having less computational work in comparison of other exiting methods. The fractional derivatives are described in the Caputo sense. The most useful advantage of this method is to solve the fractional integro-differential equation without using Adomian polynomials and He’s polynomials for the computation of nonlinear terms. AMS Subject Classification: 00A71, 45A05, 34A12, 45E10, 7Q10

Highlights

In this paper, we will study the homotopy analysis transform method (HATM) for a special kind of nonlinear fractionalReceived: October 17, 2015 Published: March 8, 2016 §Correspondence author c 2016 Academic Publications, Ltd. url: www.acadpubl.euM.S
The analytic results on existence and uniqueness of problems solutions to fractional differential equations have been investigated by many authors [3, 4]
Yang [11] applied the hybrid of block- pulse function and Chebyshev polynomials to solve nonlinear Fredholm fractional integro-differential equations

Summary

Introduction

We will study the HATM for a special kind of nonlinear fractionalReceived: October 17, 2015 Published: March 8, 2016 §Correspondence author c 2016 Academic Publications, Ltd. url: www.acadpubl.euM.S. Y(i) = δi, i = 0, 1, 2, ..., n − 1, n − 1 < α ≤ n, n ∈ N, where g ∈ L2 ([0, 1]), p ∈ L2 ([0, 1]), k ∈ L2 [0, 1]2 are known functions, y (t) is the unknown function and Dα is the Caputo fractional differential operator of order α Such equations arise in the mathematical modeling of various physical phenomena, such as heat conduction in materials with memory. The analytic results on existence and uniqueness of problems solutions to fractional differential equations have been investigated by many authors [3, 4]. Most of nonlinear fractional integro-differential equations do not have exact analytic solution, so approximation and numerical technique must be used.

Objectives

Methods

Conclusion