摘 要：科技进步带动着数学模型的发展，传统的整数阶微分方程已经难以满足人们的研究需要，分数阶微分方程在某些方面能够更准确描述一些实际现象，近几十年来得到了各个领域的应用。研究此类系统解的个数问题最常用的方法是不动点理论，但是由于分数阶微分算子的大多性质都与整数阶微分算子不同，使得一些左右混合RL 型分数阶微分方程难以适用。该文使用临界点理论有效研究了一类左右混合RL 型分数阶脉冲微分方程边值问题。
关键词：分数阶微分方程；脉冲；临界点理论
中图分类号：O175.8 文献标识码：A 文章编号：2096-4706（2020）08-0004-05
Study on Boundary Value Problems for a Class of Fractional Order Impulsive Differential Equations
PENG Yuanshuang1，CHEN Guoping1，DONG Yanjun2
（1.Jishou University，Jishou 416000，China；2.Yunnan College of Foreign Affairs & Foreign Language，Kunming 651700，China）
Abstract：Advances in science and technology have led to the further development of mathematical models. Traditional integerorder differential equations have been difficult to meet people’s research needs. However，fractional differential equations can more accurately describe some practical phenomena in some aspects. In recent decades，it has been applied in various fields. The most commonly used method for studying the number of solutions to such systems is the fixed point theory. However，most of the properties of fractional differential operators are different from integer-order differential operators，making some left-right mixed RL-type fractional differential equations difficult to apply. In this paper，we use the critical point theory to effectively study the boundary value problem of a class of left-right mixed RL-type fractional impulsive differential equations.
Keywords：fractional differential equation；impulsive；critical point theory
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作者简介：
彭元双（1989.02—），男，土家族，湖南保靖人，硕士研究生，研究方向：微分方程与动力系统；
陈国平（1964.06—），男，汉族，湖南邵阳人，教授，博士，研究方向：微分方程与动力系统研究；
董彦君（1991.07—），女，汉族，广西百色人，助教，硕士研究生，研究方向：微分方程与动力系统。