Solitary wave solutions to some nonlinear fractional evolution equations in mathematical physics

Abstract

The objective of this article is to construct new and further general analytical wave solutions to some nonlinear evolution equations of fractional order in the sense of the modified Riemann-Liouville derivative relating to mathematical physics, namely, the space-time fractional Fokas equation, the time fractional nonlinear model equation and the space-time fractional (2 þ 1)-dimensional breaking soliton equation by exerting a rather new mechanism ðG' =G; 1 =GÞ -expansion method. We use the fractional complex transformation and associate the fractional differential equations to the solvable integer order differential equations. A comprehensive class of new and broad-ranging exact traveling and solitary wave solutions are revealed in terms of trigonometric, rational and hyperbolic functions. The attained wave solutions are sketched graphically by using Mathematica and make a comparison to the results attained by the presented technique with other techniques in a comprehensive manner. It is notable that the method can be considered as a reduction of the reputed ðG' =GÞ -expansion method commenced by Wang et al. It is noticeable that, the two variable ðG' =G; 1 =GÞ -expansion method appears to be more reliable, straightforward, computerized and user-friendly.

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