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

Abstract The generalization of boundary value problems always covers a wide range of equations. Our choice in this research is the generalization of Caputo-type fractional discrete differential equations that include two or more fractional q-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVP base on some fixed point theorems, including fixed point theorem of Banach, Leray-nonlinear Schauder’s alternative, and Leray-degree Schauder’s theory. Finally, several examples are presented to demonstrate accuracy of our results. (2010) Mathematics Subject Classifications: 26A33, 34A08, 34B15.