Analysis of Delay-Type Integro-Differential Systems Described by the Φ-Hilfer Fractional Derivative

In this article, a novel type of equation, namely the Φ-Hilfer fractional-order integro-differential delay system (Φ-HFOIDDS), is proposed. Here, we study the existence and Hyers–Ulam–Mittag–Leffler (H-U-M-L) stability of the aforementioned equation which are obtained by using the multivariate Mittag–Leffler function, Banach contraction principle, and Picard operator method as well as generalized Gronwall inequality. Finally, we conclude this paper by constructing a suitable example to illustrate the applicability of the principal outcomes.