Invariant subspaces and exact solutions for a system of fractional PDEs in higher dimensions

Abstract

In this article, we develop an invariant subspace method for a system of time-fractional nonlinear partial differential equations in \((1+2)\) dimensions. Efficacy of the method is demonstrated by solving coupled system of nonlinear time-fractional diffusion equations and coupled system of time-fractional Burger’s equations in higher dimensions. Furthermore, the algorithmic approach to find more than one invariant subspace is proposed and corresponding exact solutions are constructed.

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Acknowledgements

The authors thank the anonymous referees for their valuable suggestions and comments. Sangita Choudhary acknowledges the National Board for Higher Mathematics, India, for the award of Research Fellowship.

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Correspondence to Varsha Daftardar-Gejji.

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Communicated by Vasily E. Tarasov.

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Choudhary, S., Prakash, P. & Daftardar-Gejji, V. Invariant subspaces and exact solutions for a system of fractional PDEs in higher dimensions. Comp. Appl. Math. 38, 126 (2019). https://doi.org/10.1007/s40314-019-0879-4

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Keywords

  • Invariant subspace method
  • Coupled system of time-fractional PDEs
  • Exact solutions

Mathematics Subject Classification

  • Primary: 26A33
  • Secondary: 35R11
  • 33E12
  • 34A05
  • 34A08
  • 35R15
  • 35Q53