A novel method for nonlinear fractional differential equations using symbolic computation

GÜNER Ö., Bekir A.

WAVES IN RANDOM AND COMPLEX MEDIA, cilt.27, sa.1, ss.163-170, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 1
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/17455030.2016.1213462
  • Dergi Adı: WAVES IN RANDOM AND COMPLEX MEDIA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.163-170
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

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.