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

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.

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• A refined invariant subspace method and applications to evolution equations
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Cited by in corpus (2)

• Invariant subspace method to the initial and boundary value problem of the higher dimensional nonlinear time-fractional PDEs
• Nonlinear two-component system of time-fractional PDEs in (2+1)-dimensions: Invariant subspace method combined with variable transformation