非瞬时脉冲分数阶微分方程边值问题解的存在性与唯一性  

Existence and uniqueness of solutions for boundary value problems of fractional differential equations with non-instantaneous impulses

作　　者：郑雯静 贾梅[1] 李庭乐 ZHENG Wenjing;JIA Mei;LI Tingle(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2020年第5期430-435,共6页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11171220)。

摘　　要：非瞬时脉冲所描述的突变会持续停留在一个有限的时间间隔内,这种现象在临床医学、生物工程、化学和物理等领域都普遍存在。为了能够更深刻、更精确地反映事物的变化规律,研究了一类具有非瞬时脉冲的分数阶微分方程边值问题解的存在性与唯一性。首先,通过建立与边值问题等价的积分方程,定义了算子,并证明了其全连续性;然后,运用Schauder不动点定理得到了边值问题解存在的充分条件;最后利用压缩映射原理得到解的唯一性定理。The mutation described by non-instantaneous pulses will stay in a limited time interval.This phenomenon is common in clinical medicine,bioengineering,chemistry,physics and other fields.In order to reflect the change law of things more profoundly and accurately,the existence and uniqueness of solutions for a class of boundary value problems of fractional differential equations with noninstantaneous impulses were studied.The operator was defined by establishing an integral equation equivalent to the boundary value problem,and its complete continuity was proved.By using Schauder fixed point theorem,the sufficient conditions for the existence of solutions of the boundary value problems were obtained.The uniqueness theorem of solutions was obtained by using the contraction mapping principle.

关 键 词：非瞬时脉冲 CAPUTO分数阶导数 SCHAUDER不动点定理 压缩映射原理 

分 类 号：O175[理学—数学]