Hilfer-Katugampola序列分数阶微分方程边值问题Lyapunov型不等式  

Lyapunov-type Inequality for Sequential Fractional Boundary Value Problem Involving Hilfer-Katugampola Fractional Derivative

作　　者：王林 董蝴蝶 陈港 WANG Lin;DONG Hu-die;CHEN Gang(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《数学的实践与认识》2023年第7期197-205,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11601007);安徽高校自然科学研究重点项目(KJ2020A0291)。

摘　　要：研究了Hilfer-Katugampola序列分数阶微分方程多点边值问题Lyapunov型不等式.首先,利用Hilfer-Katugampola分数阶微积分的定义和性质将HilferKatugampola序列分数阶微分方程边值问题等价转化为带有Green函数的积分方程问题.其次,定义相应的Banach空间并结合先验估计方法得到了Lyapunov型不等式.最后,通过给出一系列推论说明该文研究结果推广和丰富了已有文献相关工作.In this paper,Lyapunov-type inequality for multi-point boundary value problem of sequential fractional differential equations with Hilfer-Katugampola derivative is studied.Firstly,by using the definitions and properties of Hilfer-Katugampola fractional calculus,the boundary value problem of Hilfer-Katugampola sequential fractional differential equation is equivalent to the problem of integral equation with Green's function.Secondly,the corresponding Banach space is defined and combined with a priori estimation method,the Lyapunov-type inequality is obtained.Finally,a series of corollaries are given to illustrate that the research results of this paper extend and enrich the relevant work of the existing literature.

关 键 词：Lyapunov型不等式 序列分数阶微分方程 Hilfer-Katugampola分数阶微分 多点边值问题 

分 类 号：O175.8[理学—数学]