Tunc, CemilTunc, Osman2025-07-302025-07-3020251561-86251934-609310.1002/asjc.36452-s2.0-105001693063https://doi.org/10.1002/asjc.3645https://hdl.handle.net/20.500.14720/28067We study a nonlinear psi-Hilfer fractional-order delay integro-differentialequation (psi-Hilfer FrODIDE) that incorporatesN-multiple variable timedelays. Utilizing the psi-Hilfer fractional derivative (psi-Hilfer-FrD), we inves-tigate the Ulam-Hyers--Rassias (U-H-R), semi-Ulam-Hyers-Rassias (semi-U-H-R) and Ulam-Hyers (U-H) stability of the considered psi-Hilfer FrO-DIDE through the fixed-point method. Throughout this work, using Banach'sfixed-point theorem and the Bielecki norm, we establish three new theoremsrelated to these qualitative concepts. The theorems presented in this work arenovel and contribute to the existing literature on the Ulam-type stability of psi-Hilfer FrODIDEseninfo:eu-repo/semantics/openAccessPsi-Hilfer FrodideFixed-Point MethodH-U-RH-U StabilitySemi-H-U-RArticle