On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations

Abstract

Lie symmetry analysis and invariant subspace methods of differential equations play an important role separately in the study of fractional partial differential equations. The former method helps to derive point symmetries, symmetry algebra and admissible exact solution, while the later one determines admissible invariant subspace as well as to derive exact solution of fractional partial differential equations. In this article, a comparison between Lie symmetry analysis and invariant subspace methods is presented towards deriving exact solution of the following coupled time fractional partial differential equations: (i) system of fractional diffusion equation, (ii) system of fractional KdV type equation, (iii) system of fractional Whitham-Broer-Kaup’s type equation, (iv) system of fractional Boussinesq-Burgers equation and (v) system of fractional generalized Hirota-Satsuma KdV equation.