Symmetry Analysis and Conservation Laws for a Time-Fractional Generalized Porous Media Equation

Tianhang Gong, Wei Feng and Songlin Zhao
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Tianhang Gong: Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
Wei Feng: Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
Songlin Zhao: Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China

Mathematics, 2022, vol. 10, issue 5, 1-21

Abstract: The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann–Liouville fractional derivatives. All point symmetry groups and the corresponding optimal subgroups are determined. Then, the similarity reduction is performed to the given equation and some explicit solutions are derived. The asymptotic behaviours for the solutions are also discussed. Through the concept of nonlinear self-adjointness, the conservation laws arising from the admitted point symmetries are listed.

Keywords: time-fractional generalized porous media equation; symmetry group; conservation law; exact solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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