On the Solutions of the Space and Time Fractional Benjamin–Bona–Mahony Equation

Mirzazadeh M., EKİCİ M., Sonmezoglu A.

Iranian Journal of Science and Technology, Transaction A: Science, vol.41, no.3, pp.819-836, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1007/s40995-016-0121-9
  • Journal Name: Iranian Journal of Science and Technology, Transaction A: Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.819-836
  • Keywords: Extended trial equation method, Space and time fractional Benjamin-Bona-Mahony (BBM) equation, Exact solution, Elliptic integral function solution, Soliton solution, PARTIAL-DIFFERENTIAL-EQUATIONS, NONLINEAR EVOLUTION-EQUATIONS, TRAVELING-WAVE SOLUTIONS, 1ST INTEGRAL METHOD, TRANSFORM
  • Yozgat Bozok University Affiliated: Yes

Abstract

© 2016, Shiraz University.In this paper, the extended trial equation method is used for constructing exact solutions of fractional partial differential equations (FPDEs) in the sense of Jumarie’s modified Riemann–Liouville derivative. To convert a fractional partial differential equation into its ordinary differential equation of integer order is used the fractional complex transformation. With the aid of symbolic computation, we choose the space and time fractional Benjamin–Bona–Mahony (BBM) equation to illustrate the validity and advantages of this method. As a result, some new exact solutions including elliptic integral function solutions and soliton solutions to this problem are successfully established. The proposed approach can also be applied to other fractional partial differential equations (FPDEs).