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本文引用的文献

1
Existence results of fractional differential equations with nonlocal double-integral boundary conditions.具有非局部双重积分边界条件的分数阶微分方程的存在性结果。
Math Biosci Eng. 2023 Jan;20(3):4437-4454. doi: 10.3934/mbe.2023206. Epub 2022 Dec 26.
2
Fractional derivatives embody essential features of cell rheological behavior.分数阶导数体现了细胞流变行为的基本特征。
Ann Biomed Eng. 2003 Jun;31(6):692-9. doi: 10.1114/1.1574026.

具有单项式系数的序列分数阶微分方程的边值问题。

Boundary problems of sequential fractional differential equations having a monomial coefficient.

作者信息

Yan Debao

机构信息

School of Mathematics and Statistics, Heze University, Heze City, Shandong Province, 274000, PR China.

出版信息

Heliyon. 2024 Aug 22;10(17):e36538. doi: 10.1016/j.heliyon.2024.e36538. eCollection 2024 Sep 15.

DOI:10.1016/j.heliyon.2024.e36538
PMID:39281563
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11400968/
Abstract

The article examines sequential fractional-order differential equations composed of monomial coefficients defined as nonlinear boundary problems. The original problem is converted into an integral equation in an equivalent form. The contraction mapping principle and Krasnoselskii's fixed-point theorem are implemented to obtain two existence conditions. The problem of Ulam-Hyers stability is also investigated. An illustration is presented to showcase practical application of the obtained results.

摘要

本文研究了由单项式系数组成的序贯分数阶微分方程，将其定义为非线性边值问题。原问题被转化为一个等价形式的积分方程。运用压缩映射原理和克拉索夫斯基不动点定理得到了两个存在性条件。还研究了乌拉姆 - 海尔斯稳定性问题。给出了一个示例以展示所得结果的实际应用。