Existence and k‐Mittag–Leffler–Ulam stabilities of a Volterra integro‐differential equation via (k,ϱ)‐Hilfer fractional derivative

Abstract

In this paper, we investigate the existence, uniqueness, and analysis of two types of ‐Mittag–Leffler–Ulam stabilities in a Volterra integro‐differential fractional differential equation that involves the ‐Hilfer operator. We utilize the Banach fixed‐point theorem to establish the existence and uniqueness of solutions. We examine the stability properties, including the ‐Mittag–Leffler–Ulam–Hyers ‐ and k‐Mittag–Leffler–Ulam–Hyers–Rassias ‐ stabilities, by employing the Grönwall–Bellman inequality. Additionally, we provide an example to confirm our findings.