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

A. Louakar, A. Kajouni, K. Hilal, H. Lmou

This work explores the stability and existence of a class of fractional Langevin inclusions with impulsive and time delay effects involving φ-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. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(3) (2024), pp. 149-167