Accepted for publication in JNEEA

Homotopy Analysis Method Combined with Natural Transform for Nonlinear Partial Differential Equations

D. Ziane, H. C. Mountassir

Laboratory of mathematics and its applications LAMAP, University of Oran, Oran 31000, Algeria

Received on January 11, 2017, revised version on April 17, 2018
Accepted on April 18, 2018

Communicated by Alexander Pankov

Abstract.  In this paper, a combined form of Natural Transform Method withHomotopy Analysis Method is proposed to solve nonlinear partial differential equations. This method is called the N-Transform Homotopy Analysis Method (NTHAM). We apply the proposed method to obtain approximate analytical solutions of the proposed problems. Several examples are given to re-confirm the efficiency of the suggested algorithm.
Keywords: Elzaki transform, homotopy analysis method, fractional porous medium equation.
2010 Mathematics Subject Classification:   35A08, 44A05, 35G25, 65H20.

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