An efficient technique for higher order fractional differential equation

Ayyaz Ali; Muhammad Asad Iqbal; Qazi Mahmood Ul-Hassan; Jamshad Ahmad; Syed Tauseef Mohyud-Din

doi:10.1186/s40064-016-1905-2

An efficient technique for higher order fractional differential equation

Springerplus. 2016 Mar 5:5:281. doi: 10.1186/s40064-016-1905-2. eCollection 2016.

Authors

Ayyaz Ali¹, Muhammad Asad Iqbal¹, Qazi Mahmood Ul-Hassan², Jamshad Ahmad³, Syed Tauseef Mohyud-Din¹

Affiliations

¹ Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan.
² Department of Mathematics, Faculty of Basic Sciences, University of Wah, Wah Cantonment, Pakistan.
³ Department of Mathematics, Faculty of Sciences, University of Gujrat, Gujrat, Pakistan.

Abstract

In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.

Keywords: Fractional calculus; Kawahara equation; Modified Riemann–Liouville derivative; The [Formula: see text]-expansion method; Traveling wave solutions.