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<p>An analogue of the generalized Leibniz rule for the Gerasimov–Caputo fractional derivative of arbitrary order is obtained. This made it possible to study the group structure of the Guéant–Pu equation with a fractional Gerasimov–Caputo time derivative. In comparison with such an equation with a fractional derivative of the order of less than 1, additional symmetries of the equation are obtained, which can be used to find its analytical solutions.</p>

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Group Analysis of Equations with the Gerasimov–Caputo Derivative Using the Example of the Guéant–Pu Equation

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • Khristofor V. Yadrikhinskiy

摘要

An analogue of the generalized Leibniz rule for the Gerasimov–Caputo fractional derivative of arbitrary order is obtained. This made it possible to study the group structure of the Guéant–Pu equation with a fractional Gerasimov–Caputo time derivative. In comparison with such an equation with a fractional derivative of the order of less than 1, additional symmetries of the equation are obtained, which can be used to find its analytical solutions.