In this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana–Baleanu–Caputo fractional derivatives of orders \(0<\vartheta \leq 1\) and \(1<\vartheta \leq 2\). We structure the equivalent fractional integral equations of the proposed problems. Further, the existence and uniqueness theorems are proved with the aid of fixed point theorems of Krasnoselskii and Banach. Lastly, the paper includes pertinent examples to justify the validity of the results.

中文翻译：

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关于带有Mittag-Leffler核和非线性积分条件的分数阶导数的分数边值问题

在本文中，我们考虑了具有非线性积分条件的非线性隐式微分方程的两类边值问题，其中涉及Atangana–Baleanu–Caputo阶导数\（0 <\ vartheta \ leq 1 \）和\（1 <\ vartheta \ leq 2 \）。我们构造了所提出问题的等价分数积分方程。此外，借助于Krasnoselskii和Banach的不动点定理证明了存在性和唯一性定理。最后，本文包括相关实例以证明结果的正确性。