Existence and uniqueness of solutions for a class of fractional differential equation with lower-order derivative dependence

This study investigates boundary value problems for nonlinear fractional-order differential equations. The differential operator is interpreted in the Riemann-Liouville sense and is coupled with a non-linearrrrr term that involves the fractional derivative of the unknown function. Using the Schauder fixed point theorem, the Banach fixed point theorem, and the Leray-Schauder continuation theorem, we establish results regarding the existence and uniqueness of solutions within suitable function spaces. Additionally, we provide concrete examples of various boundary value problems involving fractional-order differential equations to demonstrate the applicability of the theory developed.