Exp(–ϕ(η))–expansion Method and Shifted Chebyshev Wavelets for Generalized Sawada-Kotera of Fractional Order

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Mohyud-Din, Syed Tauseef^* | Ali, Ayyaz

Affiliations: Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan. syedtauseefs@hotmail.com

Correspondence: [*] Address for correspondence: Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan

Abstract: We study a nonlinear generalized Sawada-Kotera equation of fractional order via the exp(–ϕ(η))–expansion method and Shifted modified Chebyshev Wavelet technique. We obtain abundant exact solutions and approximate solution of the equation. The results of the study shows that the exp(–ϕ(η))–expansion method is very effective and proficient for solving nonlinear fractional partial differential equations. The solitary wave solutions are obtained through 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 expedient for fractional PDEs, and could be extended to other physical problems. Results of the proposed methods show an excellent conformity with the exact solution of the considered problem.

Keywords: Exp(–ϕ(η))–expansion method, Legendre Wavelets Method, Generalized Sawada-Kotera equation, Soliton solutions, Fractional calculus, Caputo’s Fractional Derivative

DOI: 10.3233/FI-2017-1486

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 173-190, 2017