Tunc, CemilAlshammari, Fehaid SalemAkyildiz, Fahir Talay2025-09-032025-09-0320252504-311010.3390/fractalfract90704092-s2.0-105011746266https://doi.org/10.3390/fractalfract9070409https://hdl.handle.net/20.500.14720/28298Tunc, Cemil/0000-0003-2909-8753In this work, we address a nonlinear psi-Hilfer fractional-order Volterra integro-differential equation that incorporates n-multiple-variable time delays. Employing the psi-Hilfer fractional derivative operator, we investigate the existence of a unique solution, as well as the Ulam-Hyers-Rassias stability, semi-Ulam-Hyers-Rassias stability, and Ulam-Hyers stability of the proposed psi-Hilfer fractional-order Volterra integro-differential equation through the fixed-point approach. In this study, we enhance and generalize existing results in the literature on psi-Hilfer fractional-order Volterra integro-differential equations, both including and excluding single delay, by establishing new findings for nonlinear psi-Hilfer fractional-order Volterra integro-differential equations involving n-multiple-variable time delays. This study provides novel theoretical insights that deepen the qualitative understanding of fractional calculus.eninfo:eu-repo/semantics/openAccessPsi-Hilfer Frovi-DeUnique SolutionUHR StabilitySemi-UHR StabilityUH StabilityFixed-Point ApproachArticle