Analytic Study on Φ-Hilfer Fractional Neutral-Type Functional Integro-Differential Equations with Terminal Conditions

The current manuscript is concerned with the uniqueness and existence of a solution for a new class of Φ-Hilfer fractional neutral functional integro-differential equations (Φ-HFNFIDEs) with terminal conditions. Firstly, employing Babenko’s approach, we convert the aforesaid equation under consideration into an analogous integral equation. More precisely, using the multivariate Mittag-Leffler function, Banach contraction principle, and Krasnoselskii’s fixed-point theorem, we derive some conditions that guarantee the uniqueness and the existence of the solutions. For an illustration of our results in this manuscript, two examples are provided as well.