A new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics

Ekici, Mehmet; Sonmezoglu, Abdullah; Zayed, Elsayed M. E.

A new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics

Document Type : Research Paper

Authors

¹ Department of Mathematics, Faculty of Science and Arts, Bozok University, Yozgat, Turkey

² Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey

³ Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

Abstract

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity and advantages of the novel method. As a result, some new exact solutions including solitary wave solutions and periodic wave solutions are successfully obtained. The proposed approach can also be applied to other nonlinear FPDEs arising in mathematical physics.

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