Invariant subspace method for (m + 1)-dimensional non-linear time-fractional partial differential equations

Abstract

In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method have been systematically investigated through the (3 + 1)-dimensional generalized non-linear time-fractional diffusion-convection-wave equation along with appropriate initial conditions. This systematic investigation provides an important technique to find a large class of various types of the invariant subspaces with different dimensions for the above-mentioned equation. Additionally, we have shown that the obtained invariant subspaces help to derive a variety of exact solutions that can be expressed as the combinations of exponential, trigonometric, polynomial and well-known Mittag-Leffler functions.

arXiv comment49 pages

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Cited by in corpus (2)

• Invariant subspace method to the initial and boundary value problem of the higher dimensional nonlinear time-fractional PDEs
• Nonlinear two-component system of time-fractional PDEs in (2+1)-dimensions: Invariant subspace method combined with variable transformation