Invariant subspaces and exact solutions for some types of scalar and coupled time-space fractional diffusion equations

TL;DR

This paper extends the invariant subspace method to solve scalar and coupled time-space fractional PDEs, demonstrating its effectiveness through various complex fractional equations and deriving multiple exact solutions.

Contribution

The paper introduces an extension of the invariant subspace method for fractional PDEs and illustrates its application to multiple complex equations with explicit solutions.

Findings

Successfully applied the method to diverse fractional equations

Derived multiple exact solutions for each equation

Proved the method's effectiveness and broad applicability

Abstract

We explain how the invariant subspace method can be extended to a scalar and coupled system of time-space fractional partial differential equations. The effectiveness and applicability of the method have been illustrated through time-space (i) fractional diffusion-convection equation, (ii) fractional reaction-diffusion equation, (iii) fractional diffusion equation with source term, (iv) two-coupled system of the fractional diffusion equation, (v) two-coupled system of fractional stationary transonic plane-parallel gas flow equation and (vi) three-coupled system of fractional Hirota-Satsuma KdV equation. Also, we explicitly presented how to derive more than one exact solution of the equations as mentioned above using the invariant subspace method.