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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (1): 148-158.doi: 10.3969/j.issn.1005-3085.2022.01.011

• • 上一篇    下一篇

带有多项分数阶导数的微分方程边值问题解的存在性

李建利1,    陈丽珍2,   李  刚3   

  1. 1. 太原学院数学系，太原 030032
    2. 山西财经大学应用数学学院，太原 030006
    3. 扬州大学数学科学学院，扬州 225002
  • 出版日期:2022-02-15 发布日期:2022-04-15
  • 通讯作者: 李 刚 E-mail: gli@yzu.edu.cn
  • 基金资助:
    国家自然科学基金 (11871064).

Existence of Solutions to Boundary Value Problem of Multi-term Fractional Differential Equations

LI Jianli1,   CHEN Lizhen2,   LI Gang3   

  1. 1. Department of  Mathematics, Taiyuan Institute, Taiyuan 030032
    2. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006
    3. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002
  • Online:2022-02-15 Published:2022-04-15
  • Contact: G. Li. E-mail address: gli@yzu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11871064).

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摘要：

自然科学中的许多实际问题可以用分数阶微分方程模型来描述，并且分数阶微积分和分数阶微分方程已经成为处理某些实际问题的重要数学工具。利用压缩映象原理、Krasnoselskii不动点定理和非紧测度理论研究一类带有混合边值条件的分数阶微分方程，并获得了非线性项在满足不同的条件下方程解的存在性和唯一性结果。这些结果推广了经典的 Bagley-Torvik 方程及相关模型解的存在性定理。

关键词: 多项分数阶导数, 边值问题, Kuratowski 非紧性测度

Abstract:

It is well known that lots of practical problems can be described by the models of fractional differential equations, and the fractional calculus and fractional differential equations are important mathematical tools in dealing the practical problems. By using the contraction mapping principle, Krasnoselskii fixed-point theorem and noncompact measure theory, a class of multi-term fractional differential equations with mixed boundary condition is studied, and some existence and uniqueness results under different conditions to the nonlinear term are obtained. These results generalize the existence theorems for the classical Bagley-Torvik equation and some related models.

Key words: multi-term fractional derivative, boundary value problem, Kuratowski measure of noncompactness

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