In this article, we explore a specific class of hybrid fractional differential equations using the \(\psi \) -Caputo derivative and subject to initial value constraints. Precisely, we rigorously establish the existence and uniqueness of solutions under certain specified conditions. The foundation of our conclusions relies on renowned theorems attributed to Schauder and Banach. Additionally, we employ a fractional fixed-point theorem, as introduced by Dhage, to demonstrate the existence of a solution and approximate it through a sequence of monotonic iterations. Furthermore, we provide an in-depth analysis of two illustrative examples to showcase and support our results
