Eidinejad, ZahraSaadati, RezaAllahviranloo, TofighLi, Chenkuan2024-05-192024-05-1920232238-36031807-0302https://doi.org10.1007/s40314-023-02362-2https://hdl.handle.net/20.500.12713/5363Our main goal in this article is to investigate the Hyers-Ulam-Rassias stability (HURS) for a type of integral equation called Volterra integral equation with delay (VIE-D). First, by considering special functions such as the Wright function (WR), Mittag-Leffler function (ML), Gauss hypergeometric function (GH), H-Fox function (H-F), and also by introducing the aggregation function, we select the best control function by performing numerical calculations to investigate the stability of the desired equation. In the following, using the selected optimal function, i.e., the minimum function, we prove the existence of a unique solution and the HURS of the VI-D equation in the matrix-valued fuzzy space (MVFS) with two different intervals. At the end of each section, we provide a numerical example of the obtained results.eninfo:eu-repo/semantics/closedAccessMittag-Leffler FunctionGauss Hypergeometric FunctionWright FunctionH-Fox FunctionHu StabilityHur StabilityAggregation Function (Af)OptimalControl FunctionMinimum FunctionVolterra Integral Equation With Delay (Vie-D)Mvfb-SpacesArticle425WOS:0010125931000022-s2.0-85162182369N/A10.1007/s40314-023-02362-2Q2