Unique Solvability and Existence of Eigenvalues for a Boundary Value Problem for a Parabolic-Hyperbolic Type Equation with a Fractional Derivative

This paper investigates a boundary value problem with deviation from the characteristic (Problem $$M$$ ) for a parabolic–hyperbolic equation with a time-fractional derivative in the sense of Gerasimov–Caputo. To construct the solution of Problem $$M$$ , the first boundary value problem is solved in the parabolic part of the mixed domain, based on which the existence and uniqueness of the classical and strong solutions of Problem $$M$$ are proven. The existence of eigenvalues for the boundary value Problem $$M$$ is established.

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