Numerical solution of time- and space-fractional coupled Burgers’ equations via homotopy algorithm

Abstract

In this paper, we constitute a homotopy algorithm basically extension of homotopy analysis method with Laplace transform, namely q-homotopy analysis transform method to solve time- and space-fractional coupled Burgers’ equations. The suggested technique produces many more opportunities by appropriate selection of auxiliary parameters ℏ and n(n⩾1) to solve strongly nonlinear differential equations. The proposed technique provides ℏ and n-curves, which describe that the convergence range is not a local point effects and finds elucidated series solution that makes it superior than HAM and other analytical techniques.

Keywords

• Laplace transform method
• q-Homotopy analysis transform method
• Fractional coupled Burgers’ equations
• ℏ and n-curves