Generalized Caputo Proportional Boundary Value Langevin Fractional Differential Equations via Kuratowski Measure of Noncompactness


Samira Zerbib, Khalid Hilal, Ahmed Kajouni




This manuscript aims to discuss the existence of solutions for nonlinear boundary value Langevin fractional differential equations involving the generalized Caputo proportional fractional derivative via Kuratowski measure of noncompactness in an arbitrary Banach space. Using the measure of noncompactness approach and Mönch's fixed point theorem, we demonstrate the existence result. An illustrative example is provided as an application to illustrate our main results.