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Exact solutions of generalized nonlinear time-fractional reaction–diffusion equations with time delay

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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 for finding invariant subspaces for the generalized nonlinear 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 yield several distinct analytical solutions. We also demonstrate how to derive exact solutions for time-fractional PDEs with multiple time delays. Finally, we extend invariant subspace method to generalized time-fractional PDEs with nonlinear term involving time delay.

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Authors and Affiliations

  1. Department of Mathematics, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, India

    P. Prakash

  2. Department of Mathematics, Savitribai Phule Pune University, Pune, 411007, India

    Sangita Choudhary & Varsha Daftardar-Gejji

Authors
  1. P. Prakash
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  2. Sangita Choudhary
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  3. Varsha Daftardar-Gejji
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Correspondence to Varsha Daftardar-Gejji.

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Prakash, P., Choudhary, S. & Daftardar-Gejji, V. Exact solutions of generalized nonlinear time-fractional reaction–diffusion equations with time delay. Eur. Phys. J. Plus 135, 490 (2020). https://doi.org/10.1140/epjp/s13360-020-00445-1

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00445-1

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