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<p>The group structure of the Allen–Cahn model with the Gerasimov–Caputo time fractional derivative is investigated. Its group classification is obtained in the case of a&#xa0;nonlinear free element in the equation. For the specifications of the right-hand side found in the classification, we have derived invariant submodels and solutions of the model under study. In conclusion, a&#xa0;comparative analysis of the symmetry properties of three Allen–Cahn models is carried out: first-order in time and in cases of Riemann–Liouville and Gerasimov–Caputo fractional derivatives with respect to time.</p>

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Symmetries of fractional Allen–Cahn models with a Gerasimov–Caputo Derivative

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Sergey A. Bogoslovskiy,
  • Vladimir E. Fedorov

摘要

The group structure of the Allen–Cahn model with the Gerasimov–Caputo time fractional derivative is investigated. Its group classification is obtained in the case of a nonlinear free element in the equation. For the specifications of the right-hand side found in the classification, we have derived invariant submodels and solutions of the model under study. In conclusion, a comparative analysis of the symmetry properties of three Allen–Cahn models is carried out: first-order in time and in cases of Riemann–Liouville and Gerasimov–Caputo fractional derivatives with respect to time.