Invariant subspaces and exact solutions for some types of scalar and coupled time-space fractional diffusion equations
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 using time-space (i) fractional diffusion-convection equation, (ii) fractional reaction-diffusion equation, (iii) fractional diffusion equation with source term, (iv) two-coupled system of 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 showed how to derive more than one exact solution of the equations as mentioned above using the invariant subspace method.
Volume 96, 2022
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