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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.

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