带瞬时脉冲的分数阶非自制发展方程解的存在唯一性

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 105-113.

带瞬时脉冲的分数阶非自制发展方程解的存在唯一性

朱波^1,*(),刘立山²

¹ 山东财经大学数学与数量经济学院济南 250014
² 曲阜师范大学数学科学学院山东曲阜 273165

收稿日期:2017-09-14 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 朱波 E-mail:zhubo207@163.com
基金资助:
山东省高校科技计划项目(J16LI14);国家自然科学基金(11871302)

Existence and Uniqueness of the Mild Solutions for a Class of Fractional Non-Autonomous Evolution Equations with Impulses

Bo Zhu^1,*(),Lishan Liu²

¹ School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014
² School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165

Received:2017-09-14 Online:2019-02-26 Published:2019-03-12
Contact: Bo Zhu E-mail:zhubo207@163.com
Supported by:
the PSDPHESTP(J16LI14);the NSFC(11871302)

摘要/Abstract

摘要：

该文利用广义Banach不动点定理研究了一类带迟滞和瞬时脉冲的分数阶非自治发展方程初值问题解的存在性和唯一性，给出其解的迭代序列和误差估计并讨论了其解是连续依赖于初值的.

关键词: 分数阶非自治发展方程, 非瞬时脉冲, 预解算子, 广义Banach不动点定理

Abstract:

In this paper, we consider a class of fractional non-autonomous evolution equations with impulses and delay. By the generalized Banach fixed point theorem, we obtain some new results on the existence and uniqueness of the mild solution. An explicit iterative scheme for the mild solution and an error estimate of the approximation sequence for the initial value problem are also derived. Moreover, the unique mild solution of the problem is continuously dependent on the initial value.

Key words: Fractional non-autonomous evolution equations, Non-instantaneous impulse, Resolvent operator, Generalized Banach fixed point theorem

中图分类号:

O175

朱波,刘立山. 带瞬时脉冲的分数阶非自制发展方程解的存在唯一性[J]. 数学物理学报, 2019, 39(1): 105-113.

Bo Zhu,Lishan Liu. Existence and Uniqueness of the Mild Solutions for a Class of Fractional Non-Autonomous Evolution Equations with Impulses[J]. Acta mathematica scientia,Series A, 2019, 39(1): 105-113.

参考文献 19

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