https://doi.org/10.1140/epjs/s11734-024-01190-7
Regular Article
On the solutions of coupled nonlinear time-fractional diffusion–reaction system with time delays
1
Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India
2
Department of Nonlinear Dynamics, Bharathidasan University, 620 024, Tiruchirappalli, India
b vishnuindia89@gmail.com, p_prakash@cb.amrita.edu
Received:
27
March
2024
Accepted:
2
June
2024
Published online:
21
June
2024
In this article, we systematically explain how to apply the analytical technique called the invariant subspace method to find various types of analytical solutions for a coupled nonlinear time-fractional system of partial differential equations with time delays. Also, the present work explicitly studies a systematic way to obtain various kinds of finite-dimensional invariant vector spaces for the coupled nonlinear time-fractional diffusion–reaction (DR) system with time delays under the two distinct fractional derivatives, namely (a) the Riemann–Liouville fractional partial time derivative and (b) the Caputo fractional partial time derivative. Additionally, we provide details of deriving analytical solutions in the generalized separable form for the initial and boundary value problems (IBVPs) of the coupled nonlinear time-fractional DR system with multiple time delays through the obtained invariant vector spaces under the considered two time-fractional derivatives.
K. S. Priyendhu, P. Prakash and M. Lakshmanan have contributed equally to this work.
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