Abstract In this article, it is concerned existence of solutions to a class of nonlinear system of fractional differential equations. It is proved the existence of at least three different weak solutions through the critical point theory and the variational method. In this way, it is applied well-known theorem proved by Bonanno and Marano on the construction of the critical set of functionals with a weak compactness condition. Furthermore, the main result is demonstrated by some examples to show its validity and efficiency.

中文翻译：

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一类非线性分数阶微分方程组至少三个不同弱解的存在性

摘要 本文研究一类非线性分数阶微分方程组解的存在性。通过临界点理论和变分方法证明了至少存在三种不同的弱解。以这种方式，它应用了由 Bonanno 和 Marano 证明的众所周知的定理，用于构造具有弱紧性条件的关键泛函集。此外，通过一些例子证明了主要结果，以表明其有效性和有效性。