一类含参数分数阶q-差分方程边值问题解的存在性  

Existence of Solution for a Class of Singular Fractional q-difference Boundary Value Problem with Parameters

作　　者：郭彩霞 李华鹏 郭建敏 田海燕 GUO Cai-xia;LI Hua-peng;GUO Jian-min;TIAN Hai-yan(School of Mathematics and Statistics,Shanxi Datong University,Datong Shanxi,037009)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009

出　　处：《山西大同大学学报（自然科学版）》2022年第2期36-40,共5页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：山西省高等学校科技创新项目[2020L0475];山西大同大学博士启动基金资助项目[2018-B-25];大同市平城区科技计划立项项目[201906]、[202106];山西大同大学校级科研基金项目[2019K13];大同市科技局项目[2019154]。

摘　　要：先介绍了分数阶q-差分方程边值问题的研究背景,然后给出了一些关于q-导数和q-积分的定义与性质,利用q-差分知识详细推导了分数阶q-差分边值问题的等价积分方程,定义了积分算子,最后通过运用Banach压缩映射原理讨论了一类含参数的分数阶q-差分边值问题解的存在性。研究内容丰富了分数阶q-差分理论的应用价值,是对分数阶微积分理论的一点补充。In this paper, the research background of the boundary value problem of fractional q-difference equation is introduced and some definitions and properties of q-derivative and q-integral are given. The equivalent integral equation of fractional qdifference boundary value problems is derived in detail by using q-difference knowledge, and then the integral operator is defined.The existence of solutions for a class of fractional q-difference boundary value problems with parameters is discussed by using Banach compression mapping principle. The research content of this paper enriches the application value of fractional q-difference theory and is a supplement to fractional calculus theory.

关 键 词：q-差分 参数 边值问题 算子 BANACH压缩映射原理 

分 类 号：O175.7[理学—数学]