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<p>The paper investigates boundary value problems for an inhomogeneous moisture transfer equation with variable coefficients and Gerasimov–Caputo time-fractional derivatives of different orders. This equation is a&#xa0;generalization of the Hallaire–Luikov equation, which introduces the concept of a&#xa0;fractal rate of humidity change to explain the presence of fluxes against the humidity potential.</p><p>Assuming the existence of a&#xa0;regular solution to the first boundary value problem for a&#xa0;non-homogeneous moisture transfer equation with variable coefficients, it is possible to obtain an a&#xa0;priori estimate using the method of energy inequalities with subsequent uniqueness of the solution to this problem and its stability with respect to the right-hand side and initial conditions.</p><p>For the generalized Hallaire–Luikov equation with first-kind boundary conditions, solutions are found for a&#xa0;system of difference equations with constant coefficients using the method of lines. An a&#xa0;priori estimate is derived, which implies the convergence of the solutions to systems of ordinary differential equations with variable fractional coefficients.</p>

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Boundary value problem for a pseudohyperbolic equation with the Gerasimov–Caputo fractional derivatives of various orders

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • M. A. Kerefov,
  • S. Kh. Gekkieva

摘要

The paper investigates boundary value problems for an inhomogeneous moisture transfer equation with variable coefficients and Gerasimov–Caputo time-fractional derivatives of different orders. This equation is a generalization of the Hallaire–Luikov equation, which introduces the concept of a fractal rate of humidity change to explain the presence of fluxes against the humidity potential.

Assuming the existence of a regular solution to the first boundary value problem for a non-homogeneous moisture transfer equation with variable coefficients, it is possible to obtain an a priori estimate using the method of energy inequalities with subsequent uniqueness of the solution to this problem and its stability with respect to the right-hand side and initial conditions.

For the generalized Hallaire–Luikov equation with first-kind boundary conditions, solutions are found for a system of difference equations with constant coefficients using the method of lines. An a priori estimate is derived, which implies the convergence of the solutions to systems of ordinary differential equations with variable fractional coefficients.