title: An efficient technique for higher order fractional differential equation.
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.
authors.affiliation: Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan.
authors.forename: Ayyaz
authors.initials: A
authors.lastname: Ali
authors.affiliation: Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan.
authors.forename: Muhammad Asad
authors.initials: MA
authors.lastname: Iqbal
authors.affiliation: Department of Mathematics, Faculty of Basic Sciences, University of Wah, Wah Cantonment, Pakistan.
authors.forename: Qazi Mahmood
authors.initials: QM
authors.lastname: Ul-Hassan
authors.affiliation: Department of Mathematics, Faculty of Sciences, University of Gujrat, Gujrat, Pakistan.
authors.forename: Jamshad
authors.initials: J
authors.lastname: Ahmad
authors.affiliation: Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan.
authors.forename: Syed Tauseef
authors.initials: ST
authors.lastname: Mohyud-Din
keywords: Fractional calculus; Kawahara equation; Modified Riemann–Liouville derivative; The [Formula: see text]-expansion method; Traveling wave solutions