Existence of Solutions to a System of Fractional <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">q</mi></mrow></semantics></math></inline-formula>-Difference Boundary Value Problems

Abstract

We are investigating the existence of solutions to a system of two fractional q-difference equations containing fractional q-integral terms, subject to multi-point boundary conditions that encompass q-derivatives and fractional q-derivatives of different orders. In our main results, we rely on various fixed point theorems, such as the Leray–Schauder nonlinear alternative, the Schaefer fixed point theorem, the Krasnosel’skii fixed point theorem for the sum of two operators, and the Banach contraction mapping principle. Finally, several examples are provided to illustrate our findings.

Keywords

• fractional q-difference equations
• coupled multi-point boundary conditions
• fractional q-integrals
• existence
• uniqueness