Abstract. In this research article, a new approach based on the Fractional Reduced Differential Transform Method (FRDTM) employed to solve the nonlinear fractional Harry Dym equation. In this work we present approximate analytical solutions of the time-fractional Harry Dym equation using the FRDTM and we find exact solution of Harry Dym equation using the RDTM. The fractional derivatives are described in the Caputo sense. The FRDTM doesn't require any discretization, linearization and therefore it reduces significantly the numerical computations compare with the existing methods such as the perturbation technique, differential transform method (DTM) and the Adomian decomposition method (ADM). Also, the results we obtained in this paper are in a good agreement with the exact solutions; hence, this technique is powerful and efficient as an alternative method for finding approximate and exact solutions for nonlinear PDEs.

Received: May 7, 2014

AMS Subject Classification: 35J05, 35J10, 33E12, 33R11, 35A22

Key Words and Phrases: reduced differential transform method, Caputo fractional derivative, fractional Harry Dym equation, fractional differential equation

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