具有Hilfer分数阶脉冲微分方程边值问题解的存在性  

Existence of solutions for boundary value problems of fractional impulsive differential equations with Hilfer

作　　者：郭春静 孟凡猛 陈坤 江卫华[1] GUO Chunjing;MENG Fanmeng;CHEN Kun;JIANG Weihua(School of Sciences,Hebei University of Science and Technology,Shijiazhuang,Hebei 050018,China;Office of Academic Affairs,Shijiazhuang People’s Medical College,Shijiazhuang,Hebei 050091,China)

机构地区：[1]河北科技大学理学院,河北石家庄050018 [2]石家庄人民医学高等专科学校教务处,河北石家庄050091

出　　处：《河北科技大学学报》2023年第2期132-143,共12页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(11775169);河北省自然科学基金(A2018208171)。

摘　　要：为了拓展边值问题的基本理论,研究一类具有有限个脉冲点的Hilfer分数阶脉冲微分方程边值问题解的存在性。首先,求出微分方程等价的积分方程;其次,定义恰当的Banach空间和范数,构造合适的算子,在非线性项满足不同条件的情况下,运用Krasnoselskii不动点定理,分别得到此类边值问题存在解的充分条件;最后,通过2个实例验证研究结果的普适性。结果表明,含有Hilfer分数阶导数的脉冲微分方程边值问题的解具有存在性。运用Krasnoselskii不动点定理能够有效解决具有Hilfer分数阶脉冲微分方程边值问题解的存在性问题,丰富了分数阶微分方程理论,为解决其他类型的脉冲分数阶微分方程边值问题提供了借鉴与参考。In order to extend the basic theory of boundary value problems,the existence of solutions for a class of Hilfer fractional impulsive differential equations with finite impulsive points was studied.Firstly,the integral equation equivalent to the differential equation was obtained;Secondly,appropriate Banach spaces and norms were defined,and appropriate operators were constructed.When the nonlinear term satisfies different conditions,sufficient conditions for the existence of solutions of such boundary value problems were obtained by using Krasnoselskii fixed point theorem;Finally,two examples were used to illustrate the universality of the research results.It is shown that the solution of the boundary value problem of impulsive differential equations with Hilfer fractional derivative exists.By using the Krasnoselskii fixed-point theorem,the existence of solutions for impulsive differential equation boundary value problems with Hilfer fractional order can be effectively solved,which provides some reference for solving other types of impulsive fractional differential equation boundary value problems.

关 键 词：解析理论 脉冲 边值问题 KRASNOSELSKII不动点定理 解的存在性 

分 类 号：O175.8[理学—数学]