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.
Highlights
Nonlinear partial differential equations have shown a variety of applications in almost every field of life, such as in electromagnetics, acoustics, electrochemistry, cosmology, biological and material science [1]-[4]
Fractional differential equations can be considered as the general form of the differential equations, as they are involved with the derivatives of any real or complex order
Step 1: First, we convert the NPDE of fractional order into nonlinear ordinary differential equations using fractional complex transformation introduced by Li et al [17]
Summary
Nonlinear partial differential equations have shown a variety of applications in almost every field of life, such as in electromagnetics, acoustics, electrochemistry, cosmology, biological and material science [1]-[4]. (2014) A New Approach for the Exact Solutions of Nonlinear Equations of Fractional Order via Modified Simple Equation Method. A new approach has been developed to find the exact solutions of nonlinear partial differential equations of fractional order by the fractional complex transformation [17] and modified simple equation method [18] [19], in the sense of modified Riemann-Liouville derivative. The modified simple equation method can be applied to find the exact solutions. Two applications are being considered to find the solution of nonlinear Burgers’ equation with time-space fractional derivatives, which has the following form [5]:.
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