一类带有Katugampola分数阶积分边值条件的Hadamard型分数阶微分方程的边值问题  

Boundary Value Problems for a Class of Hadamard Type Fractional Differential Equations with Katugampola Fractional Integral Conditions

作　　者：陈奕如 顾海波[1] 马丽娜 CHEN Yi-ru;GU Hai-bo;MA Li-na(School of Mathematical Sciences,Xinjiang Normal University,Urumqi,Xinjiang,830017,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《新疆师范大学学报（自然科学版）》2020年第1期17-22,38,共7页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：国家自然科学基金(11961069);新疆维吾尔自治区自然科学基金(2019D01A71);新疆维吾尔自治区高校科研计划(XJEDU2018Y033);新疆师范大学硕士研究生科研创新项目(XSY201902002)等资助。

摘　　要：文章对一类带有Katugampola分数阶积分边值条件的Hadamard型分数阶微分方程边值问题进行了研究。与前人研究的不同之处在于针对Hadamard型分数阶微分方程给出了Katugampola分数阶积分边值条件,而Katugampola分数阶积分是近年来提出的新型积分,故所获得结果也比较新颖。文章通过使用Krasnoelkii不动点定理和Banach压缩映射原理得到边值问题解的存在性和唯一性结果。最后给出了一个例子,验证了所获得的理论结果的有效性。We study a class of Hadamard type fractional-order differential equation boundary value problems with Katugampola fractional-order integral boundary value conditions.Different from previous studies,Katugampola fractional integral is given for the boundary ralue condition of Hadamard type fractional differential equation and Katugampola fractional integral is a new type of integral proposed in resent years,so the obtained results of existence and uniqueness are relatively novel.By using Krasnoelkii fixed point theorem and Banach contraction mapping principle,the existence and uniqueness of solutions for boundary value problems are obtained.Finally,an example is given to verify the validity of the theoretical results.

关 键 词：分数阶微分方程 Hadamard导数 Katugampola导数 边值问题 

分 类 号：O175.14[理学—数学]