In this paper, a research has been done about the existence of solutions to the Dirichlet boundary value problem for -Laplacian fractional differential equations which include instantaneous and noninstantaneous impulses. Based on the critical point principle and variational method, we provide the equivalence between the classical and weak solutions of the problem, and the existence results of classical solution for our equations are established. Finally, an example is given to illustrate the major result.

中文翻译：

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具有瞬时和非瞬时脉冲的Laplacian分数Dirichlet问题的变分方法

在本文中，研究已经完成关于解的存在性，为Dirichlet边值问题-拉普拉斯分数阶微分方程，其中包括瞬时和noninstantaneous冲动。基于临界点原理和变分方法，我们给出了问题的经典解和弱解的等价关系，并建立了方程经典解的存在性结果。最后，给出一个例子来说明主要结果。