Higher-Order Symmetries of a Time-Fractional Anomalous Diffusion Equation

Rafail K. Gazizov and Stanislav Yu. Lukashchuk
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Rafail K. Gazizov: RN-BashNIPIneft LLC, 3/1 Bekhtereva Str., 450103 Ufa, Russia
Stanislav Yu. Lukashchuk: Laboratory “Group Analysis of Mathemaical Models in Natural and Engineering Sciences”, Ufa State Aviation Technical University, 12 K. Marx Str., 450008 Ufa, Russia

Mathematics, 2021, vol. 9, issue 3, 1-10

Abstract: Higher-order symmetries are constructed for a linear anomalous diffusion equation with the Riemann–Liouville time-fractional derivative of order α ∈ ( 0 , 1 ) ∪ ( 1 , 2 ) . It is proved that the equation in question has infinite sequences of nontrivial higher-order symmetries that are generated by two local recursion operators. It is also shown that some of the obtained higher-order symmetries can be rewritten as fractional-order symmetries, and corresponding fractional-order recursion operators are presented. The proposed approach for finding higher-order symmetries is applicable for a wide class of linear fractional differential equations.

Keywords: anomalous diffusion; Riemann–Liouville fractional derivative; Lie–Bäcklund transformation; higher-order symmetry; recursion operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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