Simplest equation method for some time-fractional partial differential equations with conformable derivative. (English) Zbl 1415.35275
Summary: The conformable fractional derivative was proposed by R. Khalil et al. [J. Comput. Appl. Math. 264, 65–70 (2014; Zbl 1297.26013)], which is natural and obeys the Leibniz rule and chain rule. Based on the properties, a class of time-fractional partial differential equations can be reduced into ODEs using traveling wave transformation. Then the simplest equation method is applied to find exact solutions of some time-fractional partial differential equations. The exact solutions (solitary wave solutions, periodic function solutions, rational function solutions) of time-fractional generalized Burgers equation, time-fractional generalized KdV equation, time-fractional generalized Sharma-Tasso-Olver (FSTO) equation and time-fractional fifth-order KdV equation, \((3+1)\)-dimensional time-fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation are constructed. This method presents a wide applicability to solve some nonlinear time-fractional differential equations with conformable derivative.
Keywords:
conformable fractional derivative; simplest equation method; fractional differential equations; traveling wave transformationCitations:
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