Existence Theory for Nonlinear Langevin-Type Fractional Differential Equations

Abstract

This paper is devoted to establishing the solvability of a class of nonlinear Langevin fractional differential equations subject to boundary conditions and formulated in terms of the generalized Caputo proportional fractional derivative. The study is conducted in a general Banach space setting. By combining the Kuratowski measure of noncompactness with Mönch’s fixed point theorem, we derive sufficient criteria ensuring the existence of solutions. A concrete example is presented at the end to confirm the effectiveness and practical relevance of the obtained results.