Analytical Investigation of the Existence and Ulam Stability of Integro-Differential Equations with Conformable Derivatives Under Non-Local Conditions

Fakhreddine, Seddiki
Hazaymeh, Ayman A
Aljazzazi, Mazin
Qaralleh, Reham
Bataihah, Anwar
Batiha, Iqbal M.
Hajaj, Rasha Ibrahim

International Journal of Robotics and Control Systems
Vol 5, No 2 (2025)

This study examines an integro-differential equation involving fractional conformable derivatives and non-local conditions. It proves the existence and uniqueness of mild solutions by applying the Banach fixed-point theorem. Furthermore, it demonstrates a notable result about the existence of at least one solution, backed by conditions based on the Krasnoselskii fixed-point theorem. The investigation also explores the Ulam stability of integro-differential equations. To highlight the practical relevance and robustness of the findings, an illustrative example is provided.