A New Approach for the Exact Solutions of Nonlinear Equations of Fractional Order via Modified Simple Equation Method

Muhammad Younis

Centre for Undergraduate Studies, University of the Punjab, Lahore, Pakistan.

DOI: 10.4236/am.2014.513186                

Abstract

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation method has been implemented, to find the exact solutions of these equations, in the sense of modified Riemann-Liouville derivative. For applications, the exact solutions of time-space fractional derivative Burgers’ equation and time-space fractional derivative foam drainage equation have been discussed. Moreover, it can also be concluded that the proposed method is easy, direct and concise as compared to other existing methods.

Keywords

Exact Solutions, Complex Transformation, Modified Simple Equation Method, Nonlinear Equations of Fractional Order, Fractional Calculus Theory

Conflicts of Interest

The authors declare no conflicts of interest.

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