Caputo分数阶微分方程解的唯一性
Uniqueness of Positive Solutions for the Caputo Fractional Differential Equation
DOI: 10.12677/AAM.2024.134111, PDF, 下载: 54  浏览: 103  科研立项经费支持
作者: 徐超宇, 王 颖*, 訾玉梅：临沂大学数学与统计学院，山东 临沂
关键词: Caputo分数阶微分方程；唯一性；解；Caputo Fractional Differential Equation； Uniqueness； Solution
摘要: 本文主要研究一类具有Riemann-Stieltjes边值条件的Caputo分数阶微分方程。 利用Green函数 的性质，Banach收缩原理，证明了方程解的唯一性。
Abstract: In this paper, we consider a class of the Caputo fractional differential equation with Riemann-Stieltjes integral boundary conditions. Making use of the properties of the Green function, the Banach contraction principle, uniqueness result of the equation is proved.
文章引用：徐超宇, 王颖, 訾玉梅. Caputo分数阶微分方程解的唯一性[J]. 应用数学进展, 2024, 13(4): 1210-1216. https://doi.org/10.12677/AAM.2024.134111

参考文献

[1] Cabada, A. and Hamdi, Z. (2014) Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions. Applied Mathematics and Computation, 228, 251-257.
https://doi.org/10.1016/j.amc.2013.11.057
[2] Ma, D.X. (2015) Positive Solutions of Multi-Point Boundary Value Problem of Fractional Differential Equation. Arab Journal of Mathematical Sciences, 21, 225-236.
https://doi.org/10.1016/j.ajmsc.2014.11.001
[3] Almeida, R. (2017) Caputo Fractional Derivative of a Function with Respect to Anoth- er Function. Communications in Nonlinear Science and Numerical Simulation, 44, 460-481.
https://doi.org/10.1016/j.cnsns.2016.09.006
[4] Ahmad, B., Alsaedi, A. and Alruwaily, Y. (2020) On Riemann-Stielties Integral Boundary Value Problems of Caputo-Riemann-Liouville Type Fractional Integro-Differential Equations. Filomat, 34, 2723-2738.
https://doi.org/10.2298/FIL2008723A
[5] Rehman, M. and Khan, R. (2010) Existence and Uniqueness of Solutions for Multi-Point Boundary Value Problems for Fractional Differential Equations. Applied Mathematics Letters, 23, 1038-1044.
https://doi.org/10.1016/j.aml.2010.04.033
[6] Zhang, X., Chen, P., Tian, H. and Wu, Y. (2023) The Iterative Properties for Positive Solutions of a Tempered Fractional Equation. Fractal and Fractional, 7, Article 761.
https://doi.org/10.3390/fractalfract7100761
[7] Chen, Y. and Li, H. (2021) Existence of Positive Solutions for a System of Nonlinear Ca- puto Type Fractional Differential Equations with Two Parameters. Advances in Difference Equations, 2021, Article No. 497.
https://doi.org/10.1186/s13662-021-03650-z
[8] [8] Podlubny, I. (1999) Fractional Differential Equations. Vol. 198, Academic Press, San Diego, CA.
[9] Miller, K.S. and Ross, B. (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York.

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