具有周期脉冲的分数阶发展方程周期mild解的存在性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1433-1450.

具有周期脉冲的分数阶发展方程周期mild解的存在性

李强^1,²(),刘立山^2,*()

¹ 山西师范大学数学与计算机科学学院太原 030002
² 曲阜师范大学数学科学学院曲阜 273165

收稿日期:2021-02-10 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 刘立山 E-mail:lznwnuliqiang@126.com;mathlls@163.com
作者简介:李强, E-mail: lznwnuliqiang@126.com
基金资助:
国家自然科学基金(11871302);国家自然科学基金(12061062);中国博士后科学基金(2020M682140);山西省国家科学基金会(201901D211399)

Existence of Periodic Mild Solutions for Fractional Evolution Equations with Periodic Impulses

Qiang Li^1,²(),Lishan Liu^2,*()

¹ Department of Mathematics, Shanxi Normal University, Taiyuan 030002
² School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165

Received:2021-02-10 Online:2022-10-26 Published:2022-09-30
Contact: Lishan Liu E-mail:lznwnuliqiang@126.com;mathlls@163.com
Supported by:
NNSF of China(11871302);NNSF of China(12061062);China Postdoctoral Science Foundation(2020M682140);the NSF of Shanxi China(201901D211399)

摘要/Abstract

摘要：

该文讨论了具有分段Caputo导数和周期脉冲的分数阶发展方程, 建立了具有周期脉冲的相关线性发展方程周期mild解的存在性和唯一性. 借助线性脉冲周期问题解算子的表达式, 利用算子半群理论和不动点定理, 证明了半线性脉冲周期问题周期mild解的一些新的存在性结果.

关键词: 脉冲分数阶发展方程, 周期脉冲, 周期mild解, 存在性, 紧半群

Abstract:

This paper discusses the fractional evolution equations with piecewise Caputo derivative and periodic impulses. The existence and uniqueness of periodic mild solutions for the associated linear evolution equation with periodic impulses is established. With the aid of the expression of the solution operator for the linear impulsive periodic problem, some new existence results of periodic mild solutions for semilinear impulsive periodic problems are showed by means of the operator semigroup theory and fixed point theorems.

Key words: Impulsive fractional evolution equations, Periodic impulses, Periodic mild solutions, Existence, Compact semigroup

中图分类号:

O177

李强,刘立山. 具有周期脉冲的分数阶发展方程周期mild解的存在性[J]. 数学物理学报, 2022, 42(5): 1433-1450.

Qiang Li,Lishan Liu. Existence of Periodic Mild Solutions for Fractional Evolution Equations with Periodic Impulses[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1433-1450.

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