Weak solutions for a generalized Katugampola fractional Langevin inclusion with boundary condition

We investigate weak solutions of a fractional Langevin inclusion subject to a nonlocal boundary condition and involving the generalized Katugampola-Caputo derivative. The problem is posed in a real Banach space and the multivalued nonlinearity is treated through Pettis-integrable selections. We first derive a precise integral representation for the associated linear boundary problem. The derivation identifies an explicit non-resonance denominator and yields a contraction condition that guarantees uniqueness of the auxiliary problem. We then construct the induced multivalued integral operator and combine the De Blasi measure of weak noncompactness with a Mönch-type fixed-point principle to obtain sufficient conditions for the existence of weak solutions . The estimates retain the contributions of both the dissipative term and the nonlocal boundary term. To illustrate the applicability of the theoretical results, three examples are provided in which all assumptions are verified, including the summability requirements in [Formula: see text].