This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann-Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in and are given to illustrate the theoritical results.

中文翻译：

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基于变分方法的一类新的非线性分数阶边值系统弱解的存在性。

本文涉及一类涉及左和右黎曼-利维尔分数阶导数的新型非线性分数阶边值系统的解的存在性。更准确地说，我们使用变分方法结合Bonano和Marano的临界点定理，确定了该问题的至少三个弱解的存在。另外，在和中给出了一些例子以说明理论结果。