Ulam‐type stability of <i>ψ</i> − Hilfer fractional‐order integro‐differential equations with multiple variable delays

Abstract We study a nonlinear Hilfer fractional‐order delay integro‐differential equation ( Hilfer FrODIDE) that incorporates multiple variable time delays. Utilizing the Hilfer fractional derivative ( Hilfer‐FrD), we investigate the Ulam–Hyers––Rassias (U–H–R), semi‐Ulam–Hyers–Rassias (semi‐U–H–R) and Ulam–Hyers (U–H) stability of the considered Hilfer FrODIDE through the fixed‐point method. Throughout this work, using Banach's fixed‐point theorem and the Bielecki norm, we establish three new theorems related to these qualitative concepts. The theorems presented in this work are novel and contribute to the existing literature on the Ulam‐type stability of Hilfer FrODIDEs.