Simplest equation method for some time-fractional partial differential equations with conformable derivative

被引：91

作者：

Chen, Cheng ^{[1
]}

Jiang, Yao-Lin ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 75卷 / 08期

关键词：

Conformable fractional derivative; Simplest equation method; Fractional differential equations; Traveling wave transformation; TRANSFORM;

D O I：

10.1016/j.camwa.2018.01.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2978 / 2988

页数：11

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