On a Class of Hybrid Langevin Inclusions Involving Two Generalized Fractional Derivatives

Abstract

In this paper, we study the existence of solutions for a hybrid Langevin inclusion involving a combination of φ-Hilfer and φ-Caputo fractional derivatives. To this end, we construct a new operator derived from the integral solution of the given boundary value inclusion problem and subsequently apply the hypotheses of Dhage’s fixed point theorem to this fractional operator. Finally, to support our theoretical findings, an illustrative example is provided.OPEN ACCESS Received: 13/11/2025 Accepted: 20/01/2026

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