Auxiliary Equation Method for Fractional Differential Equations with Modified Riemann-Liouville Derivative

Akbulut A., Kaplan M., Bekir A.

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, cilt.17, sa.7-8, ss.413-420, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 7-8
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1515/ijnsns-2016-0023
  • Dergi Adı: INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.413-420
  • Anahtar Kelimeler: modified Riemann-Liouville derivative, auxiliary equation method, the space-time fractional differential equations, fractional complex transform, SOLITON PERTURBATION-THEORY, KLEIN-GORDON EQUATIONS
  • Bursa Uludağ Üniversitesi Adresli: Hayır

Özet

In this work, the auxiliary equation method is applied to derive exact solutions of nonlinear fractional Klein-Gordon equation and space-time fractional Symmetric Regularized Long Wave equation. Consequently, some exact solutions of these equations are successfully obtained. These solutions are formed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. The exact solutions founded by the suggested method indicate that the approach is easy to implement and powerful.