Solvability and Stability Results for a Nonlocal Fractional q-Differential Boundary Value Problem

We establish solvability and stability criteria for nonlinear nonlocal fractional q-differential boundary value problems, together with the corresponding differential inclusion with nonlocal multipoint and integral boundary conditions, including the fractional condition. First, an equivalent fractional q-integral equation is derived. The single-valued problem’s existence is demonstrated via fixed-point methods including α–ψ-contractive and α-admissible operators, along with a Krasnosel’skii-type theorem. The uniqueness of the solution is subsequently established by means of Banach’s contraction theorem. For the associated multivalued problem, existence results are proved by means of multivalued α–ψ-contractions and an approximate endpoint criterion. Sufficient conditions for Ulam–Hyers and generalized Ulam–Hyers stability are also established. To validate the practical relevance of the established findings, two representative examples are provided.