Auxiliary equation method for time-fractional differential equations with conformable derivative

Akbulut A., Kaplan M.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.75, no.3, pp.876-882, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 75 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1016/j.camwa.2017.10.016
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.876-882
  • Keywords: Conformable fractional derivative, Auxiliary equation method, Time-fractional differential equations, 1ST INTEGRAL METHOD, TRAVELING-WAVE SOLUTIONS, NONLINEAR SCHRODINGERS EQUATION, SOLITON-SOLUTIONS, LAW NONLINEARITY, POWER-LAW, PERTURBATION, EVOLUTION
  • Bursa Uludag University Affiliated: No

Abstract

In this paper, the auxiliary equation method is applied to obtain analytical solutions of (2 + 1)-dimensional time-fractional Zoomeron equation and the time-fractional third order modified KdV equation in the sense of the conformable fractional derivative. Given equations are converted to the nonlinear ordinary differential equations of integer order; and then, the resulting equations are solved using a novel analytical method called the auxiliary equation method. As a result, some exact solutions for them are successfully established. The exact solutions obtained by the proposed method indicate that the approach is easy to implement and effective. (C) 2017 Elsevier Ltd. All rights reserved.