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具有微分算子的分数阶微分方程边值问题解的存在性与唯一性
  • ISSN号：1007-6735
  • 期刊名称：《上海理工大学学报》
  • 时间：0
  • 分类：O175.8[理学—数学;理学—基础数学]
  • 作者机构：[1]上海理工大学理学院,上海200093
  • 相关基金：国家自然科学基金资助项目（11171220）
作者： 吴贵云[1], 刘锡平[1], 杨浩[1]
关键词： Riemann-Liouville分数阶导数, 分数阶微分方程, 微分算子, 边值问题, 存在性与唯一性, Riemann,LiouviUe fractional derivative, fractional differential equation, differential operator, boundary value problem, existence and uniqueness
中文摘要：

研究一类具有分数阶线性微分算子的Riemann-Liouville型分数阶非线性微分方程两点边值问题解的存在性和唯一性.通过求出相应边值问题的Green函数并证明其性质,建立积分算子方程,应用压缩映射原理证明了这类边值问题解的存在性与唯一性定理.运用Krasnoselskii’s不动点理论建立并证明了该边值问题解的存在性与唯一性定理.最后给出了两个应用实例,用以说明本文所得结论的有效性.

英文摘要：

The existence and uniqueness of solutions for a class of two points boundary value problems of Riemann-LiouviUe nonlinear fractional differential equation with linear fractional differential operator were considered. Through finding the Green function of the boundary value problem and determining its properties,an integral operator equation was established and some sufficient conditions for the existence and uniqueness of solutions were derived by applying the contraction principle and the fixed point theorem. Some examples were given to illustrate the results.

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期刊信息
  • 《上海理工大学学报》
  • 北大核心期刊（2011版）
  • 主管单位:上海市教育委员会
  • 主办单位:上海理工大学
  • 主编：庄松林
  • 地址：上海市军工路516号489信箱
  • 邮编：200093
  • 邮箱：xbzrb@USST.edu.cn
  • 电话：021-55277251
  • 国际标准刊号：ISSN：1007-6735
  • 国内统一刊号：ISSN：31-1739/T
  • 邮发代号:4-401
  • 获奖情况:
  • 上海市高等学校优秀自然科学学报一等奖,1999年获全国优秀高等学校自然科学学报及教育部优...,1995年获机械工业部优秀科技期刊三等奖
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国化学文摘（网络版）,荷兰文摘与引文数据库,美国剑桥科学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）
  • 被引量:5359