Boundary Value Problem for a Degenerate Equation of Even Order With a Fractional Derivative in a Mixed Domain

ABSTRACT In this paper, in a rectangular domain, we study a Dirichlet‐type problem with gluing conditions for a degenerate high‐order equation with fractional derivatives in the Riemann–Liouville sense of orders , for , and , for . A criterion for the uniqueness of the solution of the stated problem is given. Using asymptotic expansions for the Mittag–Leffler function and Bessel's inequality, sufficient conditions for the existence of a solution are found.

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