期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 75, 期 8, 页码 2978-2988出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2018.01.025
关键词
Conformable fractional derivative; Simplest equation method; Fractional differential equations; Traveling wave transformation
资金
- Natural Science Foundation of China (NSFC) [11371287, 61663043]
The conformable fractional derivative was proposed by R. Khalil et al. in 2014, 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. (C) 2018 Elsevier Ltd. All rights reserved.
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