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arXiv · 2001.09409

Exact solutions of generalized non-linear time-fractional reaction-diffusion equations with time delay

P. Prakash·Sangita Choudhary·Varsha Daftardar-Gejji
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Abstract

In this paper, we propose the invariant subspace approach to find exact solutions of time-fractional partial differential equations (PDEs) with time delay. An algorithmic approach of finding invariant subspaces for the generalized non-linear time-fractional reaction-diffusion equations with time delay is presented. We show that the fractional reaction-diffusion equations with time delay admit several invariant subspaces which further yields several distinct analytical solutions. We also demonstrate how to derive exact solutions for time-fractional PDEs with multiple time delays. Finally, we extend the invariant subspace method to more generalized time-fractional PDEs with non-linear terms involving time delay.

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P. Prakash, Sangita Choudhary, Varsha Daftardar-Gejji. 2020-01-26. Exact solutions of generalized non-linear time-fractional reaction-diffusion equations with time delay. https://doi.org/10.1140/epjp/s13360-020-00445-1

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