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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

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非线性分数阶积分微分方程边值问题正解的存在性

杨晓莹,   贾  梅,   刘锡平   

  1. 上海理工大学理学院，上海 200093
  • 出版日期:2022-12-15 发布日期:2022-12-15
  • 通讯作者: 贾 梅 E-mail: jiamei-usst@163.com
  • 基金资助:
    国家自然科学基金 (11171220).

Existence of Positive Solutions for Boundary Value Problems of Nonlinear Fractional Integro-differential Equations

YANG Xiaoying,   JIA Mei,   LIU Xiping   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093
  • Online:2022-12-15 Published:2022-12-15
  • Contact: M. Jia. E-mail address: jiamei-usst@163.com
  • Supported by:
    The National Natural Science Foundation of China (11171220).

PDF (PC)

145

摘要：

研究一类具有两个分数阶导数项的非线性分数阶积分微分方程积分边值问题。首先将原问题转化为只有一个导数项的等价形式，通过定义等价问题的上下解，再利用单调迭代技术建立了原问题正解的存在性与唯一性定理，给出了求其唯一正解的迭代格式和误差估计。最后给出实例说明所得结论的有效性和适用性。

关键词: Riemann-Liouville 分数阶导数, 积分微分方程, 边值问题, 上下解, 误差估计

Abstract:

The integral boundary value problem for a class of nonlinear fractional integro-differential equations with two fractional derivative terms is studied. Firstly, the original problem is transformed into an equivalent form with only one derivative term. The existence and uniqueness theorems of positive solutions of the original problem are established by defining the upper and lower solutions of the equivalent problem and using the monotone iterative technique. The iterative schemes and error estimates for finding the unique solutions are obtained. Finally, an example is presented to illustrate the effectiveness and potential applications of our main results.

Key words: Riemann-Liouville fractional derivatives, integro-differential equations, boundary value problems, upper and lower solutions, error estimation

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