Existence and stability results to a class of $\psi$-Hilfer fractional Langevin inclusions with impulsive and time delay

This work explores the stability and existence of a class of fractional Langevin inclusions with impulsive and time delay effects involving $\psi$-Hilfer derivative. We establish the existence conditions for solutions using the Covitz-Nadler fixed-point theorem. The Picard operator method and a recently developed generalized Gronwall inequality are employed in Ulam stability analysis. We provide a thorough example to illustrate the applicability of our theoretical results.