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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Exact Solutions of Time-Space Fractional Differential Equations using Invariant Subspace Method

Journal of Applied Nonlinear Dynamics 15(3) (2026) 667--681 | DOI:10.5890/JAND.2026.09.010

Reetha Thomas, T. Bakkyaraj

Indian Institute of Information Technology Kottayam, Pala, Valavoor P.O, Kottayam-686635, Kerala, India

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Abstract

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.

Acknowledgments

One of the authors (Reetha Thomas) would like to thank the Council of Scientific and Industrial Research (CSIR), Government of India, New Delhi, for providing Direct Senior Research Fellowship (Direct SRF).

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