Lie point symmetry for space-fractional porous medium equation in terms of the Riesz-fractional derivative

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2025年6月1日

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F. S. Costa,
A. L. C. Oliveira,
J. V. C. Sousa,
J. C. A. Soares

摘要

The theory of nonlocal fractional operators concerning the singular kernel involving the function $\psi (\cdot )$ $ψ (\cdot)$ has drawn attention, in particular, the relation between fractional calculus and Lie symmetries. In this paper, we discuss new infinitesimal extensions for fractional and fractional differential operators of the types $\psi $ $ψ$ -Riemann–Liouville and $\psi $ $ψ$ -Hilfer. In this sense, some particular cases and observations are presented to clarify the paper’s objectives. The Lie symmetries are obtained for the space-fractional porous medium equation, and its similarity solutions are derived.