Dirichlet-Type Problem for an Even-Order Degenerate Equation with Gerasimov–Caputo Fractional Derivative

In this paper, a boundary value problem of the Dirichlet type is investigated for a degenerate inhomogeneous equation of even order with Gerasimov–Caputo derivative. The solution is constructed as a series in eigenfunctions of a one-dimensional spectral problem for a degenerate equation of even order. When constructing a solution to the problem, a boundary value problem for a one-dimensional equation of fractional order is also investigated depending on the sign of the constant coefficient $$q$$ of the equation, and necessary estimates of the solution are obtained. Sufficient conditions are found for the convergence of the series that is a solution of the Dirichlet problem and the series obtained by differentiation. The uniqueness of the solution is shown by the spectral method.

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