Existence and generalized Ulam-Hyers-Rassias stability of implicit nonlocal problems involving the Hilfer-Katugampola fractional derivative

M. S. Souid, B. Telli, I. N. Telli, E. El-hady

In this study, we explore the presence of solutions for nonlocal initial value problems involving implicit differential equations featuring the Hilfer-Katugampola fractional derivative. We establish the Ulam-Hyers stability for the solutions of these equations within the weighted space Ch,ρ[a,b]. To demonstrate our findings, we provide several illustrative examples. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(2) (2026), pp. 141-160