Abstract:
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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