J. Nonl. Evol. Equ. Appl. 2015 (6), pp. 91-104, published on March 7, 2016:

Applications of Homotopy perturbation method and Elzaki transform for Solving Nonlinear Partial Differential Equations of fractional order

A. Neamaty, B. Agheli, R. Darzi

Department of Mathematics, University of Mazandaran, Babolsar, Iran

Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran

Received on February 1, 2015, revised version on July 31, 2015
Accepted on July 31, 2015

Communicated by Mouffak Benchohra

Abstract.  In this paper a reliable combination of homotopy perturbation method and Elzaki transform has been presented for the purpose of investigating some nonlinear partial differential equations of fractional order. We have shown that through using homotopy perturbation method, we can handle the nonlinear terms. Further, we have applied this suggested homotopy perturbation method in order to reformulate initial value problem. The application of this method results in the solution regarding transformed variables. Besides, the series solution is obtained through using the inverse transformation. The results obtained shows the efficiency of the proposed method.
Keywords:Homotopy Perturbation Methods; Elzaki transform; Time-fractional partial differential equation; He’s Polynomials.
2010 Mathematics Subject Classification:   65H20, 35R11.

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