Numerical treatment for the solution of fractional fifth-order Sawada–Kotera equation using second kind Chebyshev wavelet method

• A method based on Chebyshev wavelet expansion has been proposed.
• The proposed method is well suited for fractional Sawada–Kotera equation.
• The results of this method have been compared with homotopy analysis method.
• There is a good agreement of results between these two methods.
• Fractional Sawada–Kotera equation has been first time solved by this method.

In this paper, a new method based on the Chebyshev wavelet expansion together with operational matrices of fractional integration and derivative of wavelet functions is proposed to solve time-fractional fifth-order Sawada–Kotera (SK) equation. Two-dimensional Chebyshev wavelet method is applied to compute the numerical solution of nonlinear time-fractional Sawada–Kotera equation. The approximate solutions of nonlinear time fractional Sawada–Kotera equation thus obtained by Chebyshev wavelet method are compared with the exact solutions as well as homotopy analysis method (HAM). The present scheme is very simple, effective and convenient for obtaining numerical solution of fractional Sawada–Kotera equation.