Nonlinear fractional \(q\)-difference equation with fractional Hadamard and quantum integral nonlocal conditions (Q2211428)

Summary: In this paper, we establish existence and uniqueness results for a boundary value problem consisting by a nonlinear fractional \(q\)-difference equation subject to a new type of boundary condition, combining the fractional Hadamard and quantum integrals. Our analysis is based on Banach's fixed point theorem, a fixed point theorem for nonlinear contractions, Krasnosel'ski i's fixed point theorem, and Leray-Schauder nonlinear alternative. Examples are given to illustrate our results.