article

Homotopy analysis method for systems of fractional integro-differential equations

Authors:

Mohammad Zurigat,

Ahmad AlawnehAuthors Info & Claims

Neural, Parallel & Scientific Computations, Volume 17, Issue 2

Pages 169 - 186

Published: 01 June 2009 Publication History

Abstract

In this article, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve systems of fractional integro-differential equations. Comparing with the exact solution, the HAM provides us with a simple way to adjust and control the convergence region of the series solution by introducing an auxiliary parameter h. Four examples are tested using the proposed technique. It is shown that the solutions obtained by the Adomian decomposition method (ADM) are only special cases of the HAM solutions. The present work shows the validity and great potential of the homotopy analysis method for solving linear and nonlinear systems of fractional integro-differential equations. The basic idea described in this article is expected to be further employed to solve other similar nonlinear problems in fractional calculus.

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Cited By

Deif SGrace S(2016)Iterative refinement for a system of linear integro-differential equations of fractional typeJournal of Computational and Applied Mathematics10.1016/j.cam.2015.08.008294:C(138-150)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1016/j.cam.2015.08.008

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Published In

cover image Neural, Parallel & Scientific Computations

Neural, Parallel & Scientific Computations Volume 17, Issue 2

Special issue on computational techniques for differential equations will applications

June 2009

114 pages

ISSN:1061-5369

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Publisher

Dynamic Publishers, Inc.

United States

Publication History

Published: 01 June 2009

Received: 10 February 2009

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Cited By

Deif SGrace S(2016)Iterative refinement for a system of linear integro-differential equations of fractional typeJournal of Computational and Applied Mathematics10.1016/j.cam.2015.08.008294:C(138-150)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1016/j.cam.2015.08.008

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