Atangana–Baleanu–Caputo differential equations with mixed delay terms and integral boundary conditions

In this research work, we investigate a class of Atangana–Baleanu–Caputo (ABC) differential equations (DEs) having proportional and discrete delay terms accompanied by integral boundary conditions. We study the two important aspects, that is, existence solution stability analysis for problem mentioned above. confirm at least one via Schaefer's fixed-point theorem its uniqueness Banach's theorem. Moreover, analysis, use concept Hyers–Ulam stability. For application purposes, apply main results to numerical specific values parameters involved.