Abstract
In this paper, the (G0/G)-expansion method is presented for finding the exact solutions of the space-time fractional traveling wave solutions for the Joseph-Egri (TRLW) equation and Gardner equation. The fractional derivatives are described by modified Riemann-Liouville sense. Many exact solutions are obtained by the hyperbolic functions, the trigonometric functions and the rational functions. This method is effcient and powerful in performing a solution to the fractional partial differential equations. Also, the method reduces the large amount of calculations
Highlights
IntroductionFractional partial di¤erential equations which are generalizations of classical partial di¤erential equations of integer order have been the focus of many studies [1, 2, 3]
Many exact solutions are obtained by the hyperbolic functions, the trigonometric functions and the rational functions
In recent years, fractional partial di¤erential equations which are generalizations of classical partial di¤erential equations of integer order have been the focus of many studies [1, 2, 3]
Summary
Fractional partial di¤erential equations which are generalizations of classical partial di¤erential equations of integer order have been the focus of many studies [1, 2, 3]. The (G0 =G)-expansion method [16, 17] to solve nonlinear fractional di¤erential equations in the sense of modi...ed Riemann-Liouville derivative by Jumarie is used [18]. Exact traveling wave solutions, (G0 =G)-expansion method, space-time fractional partial di¤erential equations,modi...ed Riemann-Liouville derivative. Where u = u(x; t) is an unknown function, and P is a polynomial of u = u(x; t) and its partial fractional derivatives, in which the highest order derivatives and the nonlinear terms are involved Li and He [20, 21] proposed a fractional complex transform to convert fractional di¤erential equations into ordinary di¤erential equations, so all analytical methods which are devoted to the advanced calculus can be applied to the fractional calculus.
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