A novel method for nonlinear fractional differential equations using symbolic computation

GÜNER Ö., Bekir A.

WAVES IN RANDOM AND COMPLEX MEDIA, vol.27, no.1, pp.163-170, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1080/17455030.2016.1213462
  • Journal Name: WAVES IN RANDOM AND COMPLEX MEDIA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.163-170
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this paper, a new approach, namely an ansatz method is applied to find exact solutions for nonlinear fractional differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to solve the fractional-order biological population model and the space-time fractional modified equal width equation, and as a result, some dark soliton solutions for them are established.