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, vol.17, no.7-8, pp.413-420, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 7-8
  • Publication Date: 2016
  • Doi Number: 10.1515/ijnsns-2016-0023
  • Journal Name: INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.413-420
  • Keywords: modified Riemann-Liouville derivative, auxiliary equation method, the space-time fractional differential equations, fractional complex transform, SOLITON PERTURBATION-THEORY, KLEIN-GORDON EQUATIONS

Abstract

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.