https://doi.org/10.1140/epjp/s13360-020-00445-1
Regular Article
Exact solutions of generalized nonlinear time-fractional reaction–diffusion equations with time delay
1
Department of Mathematics, Amrita Vishwa Vidyapeetham, 641112, Coimbatore, India
2
Department of Mathematics, Savitribai Phule Pune University, 411007, Pune, India
c
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Received:
7
April
2020
Accepted:
12
May
2020
Published online:
10
June
2020
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
