In this paper, we establish existence and uniqueness results for a boundary value problem consisting by a nonlinear fractional -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 ’s fixed point theorem, and Leray-Schauder nonlinear alternative. Examples are given to illustrate our results.

中文翻译：

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分数Hadamard和量子积分非局部条件的非线性分数差分方程。

在本文中，我们建立存在唯一性结果由通过非线性分数的边界值问题-差分方程受到一种新型的边界条件，结合分数哈达玛和量子积分。我们的分析基于Banach的不动点定理，非线性收缩的不动点定理，Krasnosel'ski的不动点定理和Leray-Schauder非线性替代方案。举例说明了我们的结果。