NONLOCAL PROBLEM FOR A MIXED TYPE FOURTH-ORDER DIFFERENTIAL EQUATION WITH HILFER FRACTIONAL OPERATOR
The paper establishes existence and uniqueness criteria for solutions to a mixed-type, fourth-order differential equation involving the Hilfer fractional operator. It utilizes the spectral method and separation of variables, and addresses the "small denominators" problem to ensure solution stability for regular spectral parameter values. The research provides a theoretical foundation for understanding and solving this class of mathematical problems.