On solutions of nonlinear time-space fractional Swift–Hohenberg equation: A comparative study

Abstract

In this paper, a comparison for the solutions of nonlinear Swift–Hohenberg equation with time-space fractional derivatives has been analyzed. The two most promising techniques, fractional variational iteration method (FVIM) and the homotopy analysis method have been chosen for the comparison. The two different definitions of fractional calculus are considered to solve time-fractional derivative separately for the considered approaches. Also, the space fractional derivative is described in the Reisz sense. Analytical and numerical solutions for various combinations of the parameters are obtained. Numerical comparisons have been made for different values of parameters and depicted.

Keywords

• Swift–Hohenberg (S–H) equation
• Reisz derivative
• Caputo derivative
• Fractional variational iteration method
• Homotopy analysis method