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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

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Volume 17, Issue 7-8


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

Arzu Akbulut
  • Corresponding author
  • Department of Mathematics-Computer, Art-Science Faculty, Eskisehir Osmangazi University, Eskisehir, Turkey
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/ Melike Kaplan / Ahmet Bekir
Published Online: 2016-11-11 | DOI: https://doi.org/10.1515/ijnsns-2016-0023


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.

Keywords: modified Riemann–Liouville derivative; auxiliaryequation method; the space-time fractional differential equations,fractional complex transform

PACS: 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg


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About the article

Received: 2016-02-09

Accepted: 2016-10-07

Published Online: 2016-11-11

Published in Print: 2016-12-01

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 17, Issue 7-8, Pages 413–420, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0023.

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