Existence of solutions to a fractional differential equation involving the Caputo q-derivative with boundary conditions in Banach spaces

Generalized boundary value problems (BVP) typically cover a wide range of equations. In this study, we focus on a generalization of Caputo-type fractional discrete differential equations that involve two or more fractional q-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVP based on several fixed point theorems, including the Banach fixed point theorem, the nonlinear Leray-Schauder alternative, and the Leray-Schauder degree theory. Finally, several examples are presented to illustrate the accuracy of our results.