(2)The double auxiliary equations method and its application to space-time fractional nonlinear equations
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L.A. Alhakim a,b, A.A. Moussa a,b,*
a Unit of Mathematics and Statistic, College of Business & Economics, Qassim University, Buraidah, Saudi Arabia
b Thoeoretical Reseach Group, Department of Mathematics, Faculty of Science, Damascus University, Damascus, Syria
Received 1 September 2018; received in revised form 1 December 2018; accepted 9 December 2018
Available online 14 December 2018
Abstract
This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation. The proposed scheme has been successfully applied on two very important evolution equations, the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation. The obtained results show that the proposed method is more powerful, promising and convenient for solving nonlinear fractional differential equations (NFPDEs). To our knowledge, the solutions obtained by the proposed method have not been reported in former literature.
© 2018 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Double auxiliary equations method; Fractional partial differential equation; Exact solution; Traveling wave solution;
Nonlinear low-pass electrical Transmission lines; Fractional Burger’s equation.