School of Mathematics and Statistics, Heze University, Heze 274000, China.
Math Biosci Eng. 2023 Jan;20(3):4437-4454. doi: 10.3934/mbe.2023206. Epub 2022 Dec 26.
This article presents the existence outcomes concerning a family of singular nonlinear differential equations containing Caputo's fractional derivatives with nonlocal double integral boundary conditions. According to the nature of Caputo's fractional calculus, the problem is converted into an equivalent integral equation, while two standard fixed theorems are employed to prove its uniqueness and existence results. An example is presented at the end of this paper to illustrate our obtained results.
本文给出了一类含有 Caputo 分数阶导数的奇异非线性微分方程的存在性结果，该方程具有非局部双重积分边界条件。根据 Caputo 分数阶微积分的性质，将问题转化为等价的积分方程，同时利用两个标准的不动点定理证明了其唯一性和存在性结果。最后给出了一个例子来说明我们得到的结果。
