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On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems

Department of High Performance Computing Technologies and Systems, Ufa State Aviation Technical University, 12 K. Marx Str., Ufa 450008, Russia
Academic Editor: Viktor N. Orlov
Mathematics 2022, 10(13), 2319; https://doi.org/10.3390/math10132319
Received: 5 June 2022 / Revised: 24 June 2022 / Accepted: 30 June 2022 / Published: 2 July 2022
(This article belongs to the Section Mathematical Physics)
The problem of finding Lie point symmetries for a certain class of multi-dimensional nonlinear partial fractional differential equations and their systems is studied. It is assumed that considered equations involve fractional derivatives with respect to only one independent variable, and each equation contains a single fractional derivative. The most significant examples of such equations are time-fractional models of processes with memory of power-law type. Two different types of fractional derivatives, namely Riemann–Liouville and Caputo, are used in this study. It is proved that any Lie point symmetry group admitted by equations or systems belonging to considered class consists of only linearly-autonomous point symmetries. Representations for the coordinates of corresponding infinitesimal group generators, as well as simplified determining equations are given in explicit form. The obtained results significantly facilitate finding Lie point symmetries for multi-dimensional time-fractional differential equations and their systems. Three physical examples illustrate this point. View Full-Text
Keywords: fractional differential equation; Lie point symmetry group; linearly autonomous symmetry fractional differential equation; Lie point symmetry group; linearly autonomous symmetry
MDPI and ACS Style

Lukashchuk, S.Y. On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems. Mathematics 2022, 10, 2319. https://doi.org/10.3390/math10132319

AMA Style

Lukashchuk SY. On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems. Mathematics. 2022; 10(13):2319. https://doi.org/10.3390/math10132319

Chicago/Turabian Style

Lukashchuk, Stanislav Yu. 2022. "On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems" Mathematics 10, no. 13: 2319. https://doi.org/10.3390/math10132319

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