WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Exact Solutions for Fractional Partial Differential Equations by an Extended Fractional Riccati Sub-Equation Method
Authors: ,
Abstract: In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary differential equations, whose solutions can be expressed in certain forms composed of the solutions of the fractional Riccati equation. As for applications of this method, we apply it to the space-time fractional Whitham-Broer- Kaup (WBK) equations and the space-time fractional Fokas equation. With the aid of the mathematical software Maple, some new exact solutions for the two equations are successfully obtained.
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Keywords: Fractional Riccati sub-equation method, Fractional partial differential equations, Exact solutions, Modified Riemann-Liouville derivative, Fractional Whitham-Broer-Kaup (WBK) equations, Fractional Fokas equation
Pages: 952-961
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #93