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Invariant subspace method and exact solutions of the coupled system of time-fractional convection–reaction–diffusion equations

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Abstract

In this paper, we present how to apply the invariant subspace method for finding the linear invariant product spaces and exact solutions of the coupled system of time-fractional nonlinear partial differential equations (NPDEs). We study how the invariant subspace method helps to reduce the coupled system of time-fractional NPDEs into the system of time-fractional ODEs. More specifically, we demonstrate the applicability and efficiency of this method by constructing different finite-dimensional linear invariant product spaces for the nonlinear coupled system of time-fractional convection–reaction–diffusion equations. Additionally, we explain how to find the exact solutions of the quadratic and cubic nonlinear coupled system of time-fractional convection–reaction–diffusion equations along with appropriate initial and boundary conditions. Also, we present 2D and 3D plots for some obtained analytical solutions with different values of fractional orders \(\alpha _i,i=1,2.\) In addition, we observe that the obtained analytic solutions can be expressed in terms of Mittag–Leffler, polynomial, exponential, and trigonometric functions.

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Acknowledgements

The authors wish to thank the anonymous referees for their constructive suggestions. The second author (K.S.P.) would like to thank the International Mathematical Union (IMU), Germany, for providing financial support in the form of IMU Breakout Graduate fellowship-2023 (IMU-BGF-2023-06).

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Correspondence to P. Prakash.

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Communicated by Kai Diethelm.

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Prakash, P., Priyendhu, K.S. & Meenakshi, M. Invariant subspace method and exact solutions of the coupled system of time-fractional convection–reaction–diffusion equations. Comp. Appl. Math. 43, 30 (2024). https://doi.org/10.1007/s40314-023-02540-2

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