IJPAM: Volume 106, No. 4 (2016)

SOLVING FRACTIONAL INTEGRO DIFFERENTIAL
EQUATIONS BY HOMOTOPY ANALYSIS
TRANSFORM METHOD

Mohamed S. Mohamed$^1$, Muteb R. Alharthi$^2$, Refah A. Alotabi$^3$
$^{1,2,3}$Mathematics Department
Faculty of Science
Taif University
Hawia, 888 Taif, SAUDI ARABIA
$^1$Mathematics Department
Faculty of Science
Al-Azhar University
Nasr City, 11448, Cairo, EGYPT


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.

Received: October 17, 2015

AMS Subject Classification: 00A71, 45A05, 34A12, 45E10, 7Q10

Key Words and Phrases: homotopy analysis transforms method, fractional integro-differential equations, Laplace decomposition method

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DOI: 10.12732/ijpam.v106i4.6 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 4
Pages: 1037 - 1055


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