一类分数阶积分微分方程PC-mild解的存在唯一性  

Existence and uniqueness of PC-mild solutions for a class of fractional integro-differential equations

作　　者：宋玉莹 马小丽 SONG Yu-ying;MA Xiao-li(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China;Lanzhou No.3 middle school,Lanzhou 730000,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070 [2]兰州市第三中学,甘肃兰州730000

出　　处：《陕西理工大学学报（自然科学版）》2022年第4期47-52,共6页Journal of Shaanxi University of Technology:Natural Science Edition

摘　　要：研究具有非瞬时脉冲的分数阶积分微分方程初边值问题,运用μ型扇形算子将其转化为Banach空间中的抽象形式,利用Banach压缩映射原理及Krasnoselskii’s不动点定理得到方程PC-mild解的存在唯一性。在运用Banach压缩映射原理证明方程PC-mild解唯一性的过程中,仅需要对一算子提出相应的条件,而不需要额外的条件去保证其他算子的压缩系数。改进了已有的相关工作。The initial boundary value problem of fractional integro-differential equation with non-instantaneous impulses is studied. It is transformed into an abstract form in Banach space by using sectorial operator of type μ. The existence and uniqueness of PC-mild solution for equation is obtained by using the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem. In the process of proving the uniqueness of PC-mild solution of the equation by using the Banach contraction mapping principle, it is only necessary to put forward the corresponding conditions for one operator without additional conditions to ensure the compression coefficients of other operators, so as to improve the existing related works.

关 键 词：非瞬时脉冲 PC-mild解 BANACH压缩映射原理 Krasnoselskii’s不动点定理 

分 类 号：O175.6[理学—数学]