Nonlinear Fractional q-Difference Equation with Fractional Hadamard and Quantum Integral Nonlocal Conditions.

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. [ABSTRACT FROM AUTHOR]