TITLE:
A New Approach for the Exact Solutions of Nonlinear Equations of Fractional Order via Modified Simple Equation Method
AUTHORS:
Muhammad Younis
KEYWORDS:
Exact Solutions, Complex Transformation, Modified Simple Equation Method, Nonlinear Equations of Fractional Order, Fractional Calculus Theory
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.13,
July
10,
2014
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.