Boundary value problems of nonlinear fractional $q$-difference (integral) equations with two fractional orders and four-point nonlocal integral boundary conditions

Abstract

This paper investigates the existence of solutions for nonlinear fractional $q$-difference equations and $q$-difference integral equations involving two fractional orders with four-point nonlocal
integral boundary conditions. The existence results are obtained by applying some traditional tools of fixed point theory, and are illustrated with examples.