On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces

Abstract

The generalization of BVPs 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 BVPs base on fixed point theory, 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.

Keywords

• Nonliner fractional equation
• Leray-Shauders alternative
• Existence
• q-R-L integral