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

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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 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.

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Acknowledgements

The author wishes to thank the editor and anonymous referees for their constructive suggestions. The author also would like to thank R Sahadevan, CSIR Emeritus Scientist, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India, for his helpful comments and suggestions for the significant improvement of the manuscript.

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  1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore,  641 112, India

    P Prakash

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  1. P Prakash
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Prakash, P. Invariant subspaces and exact solutions for some types of scalar and coupled time-space fractional diffusion equations. Pramana - J Phys 94, 103 (2020). https://doi.org/10.1007/s12043-020-01964-3

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  • DOI: https://doi.org/10.1007/s12043-020-01964-3

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