Based on the group analysis of differential equations, we consider the symmetry properties of equations with fractal derivatives defined within the framework of Fα-calculus. Analogs of the prolongation of transformations of independent and dependent variables are discussed. The infinitesimal invariance of equations with fractal derivatives is studied on an example of the Lie symmetries of the one-dimensional diffusion equation with a fractal time derivative.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 122–131, April, 2021.
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Shapovalov, A.V., Brons, R. Invariance Properties of the One-Dimensional Diffusion Equation with a Fractal Time Derivative. Russ Phys J 64, 704–716 (2021). https://doi.org/10.1007/s11182-021-02371-w
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DOI: https://doi.org/10.1007/s11182-021-02371-w