An investigation into the characteristics of VFIDEs with delay: solvability criteria, Ulam–Hyers–Rassias and Ulam–Hyers stability

This article mainly focuses on studying a class of novel nonlinear Volterra-Fredholm-type integro-differential equations(VFIDE) with delay. The primary purpose of the study is to obtain results concerning Ulam–Hyers–Rassias Stability and Ulam–Hyers Stability. Additionally, the article establishes the existence of unique solutions for the considered type VFIDE. Applying the Banach contraction mapping principle without imposing strict assumptions enhances the study’s suitability for qualitative analysis. Two examples are presented to validate the proposed developments and the outcomes are visually represented through graphical illustrations.