Exact Solutions of Time-Space Fractional Differential Equations using Invariant Subspace Method
DOI:
https://doi.org/10.5890/JAND.2026.09.010Abstract
In the present work, we systematically derive the invariant subspaces for nonlinear time-fractional differential equations in the Hilfer sense and illustrate its applicability through physically significant equations such as the time-fractional heat equation, time fractional Burgers equation, time fractional KdV equation, and time fractional Hunter Saxton equation in the Hilfer sense. We also propose the invariant subspace method to time-space fractional partial differential equations involving the one-dimensional fractional Laplacian. We consider the representation of fractional Laplacian as self-induced one-dimensional Riesz potential. Our investigation reveals that linear fractional partial differential equations with the one-dimensional Riesz potential admit the exponential type invariant subspaces. Furthermore, we explore various forms of quadratic nonlinear fractional differential equations that admit the exponential invariant subspaces.References
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