一类混合型分数阶半线性积分-微分方程解的存在性

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1334-1341.

一类混合型分数阶半线性积分-微分方程解的存在性

朱波^1,*(),韩宝燕²,刘立山³

¹ 山东财经大学数学与数量经济学院济南 250014
² 山东工艺美术学院公共教学部济南 250014
³ 曲阜师范大学数学科学学院山东曲阜 273165

收稿日期:2018-08-29 出版日期:2019-12-26 发布日期:2019-12-28
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 of Mild Solutions for a Class of Fractional Semilinear Integro-Differential Equation of Mixed Type

Bo Zhu^1,*(),Baoyan Han²,Lishan Liu³

¹ School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014
² Common Course Teaching Department, Shandong University of Art and Design, Jinan 250014
³ School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165

Received:2018-08-29 Online:2019-12-26 Published:2019-12-28
Contact: Bo Zhu E-mail:zhubo207@163.com
Supported by:
the PSDPHESTP(J16LI14);the NSFC(11871302)

摘要/Abstract

摘要：

该文利用非紧性测度、β-预解族、k-集压缩原理研究了一类混合型分数阶半线性积分-微分方程温和解的存在性.众所周知，利用k-集压缩原理证明解的存在性时需要单独给出附加条件来保证压缩系数小于1，而该文不需要单独附加保证压缩系数小于1的条件.在更一般的条件下证明了方程解的存在性.文章最后给出了一个例子说明该文主要结果的应用.

关键词: 混合型分数阶半线性积分-微分方程, k-集压缩, 非紧性测度, β-预解族

Abstract:

In this paper, the authors studied the existence results of the mild solutions for a class of fractional semilinear integro-differential equation of mixed type by using the measure of noncompactness, k-set contraction and β-resolvent family. It is well known that the k-set contraction requires additional condition to ensure the contraction coefficient 0 < k < 1. We don't require additional condition to ensure the contraction coefficient 0 < k < 1. An example is introduced to illustrate the main results of this paper.

Key words: Fractional semilinear integro-differential equation of mixed type, k-Set contraction, Measure of noncompactness, β-Resolvent family

中图分类号:

O175

朱波,韩宝燕,刘立山. 一类混合型分数阶半线性积分-微分方程解的存在性[J]. 数学物理学报, 2019, 39(6): 1334-1341.

Bo Zhu,Baoyan Han,Lishan Liu. Existence of Mild Solutions for a Class of Fractional Semilinear Integro-Differential Equation of Mixed Type[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1334-1341.

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