Existence Results for Generalized Caputo Proportional-Type Fractional Langevin Equations with p-Laplacian operator via Measure of Noncompactness

Résumé

This study addresses the existence of solutions for a novel class of generalized Caputo proportional-type fractional differential Langevin equations involving the p-Laplacian operator. The analysis is conducted by integrating the theory of the p-Laplacian operator with essential concepts from fractional calculus. Using the Kuratowski measure of noncompactness in an arbitrary Banach space and applying Mönch's fixed point theorem within the framework of the measure of noncompactness approach, we establish existence results. To illustrate the applicability and effectiveness of the proposed method, a detailed example is presented.