University of 8 May 1945 Guelma, Guelma, Algeria.
Laboratory of Analysis and Control of Differential Equations "ACED", Department of Mathematics, Faculty MISM, University of 8 May 1945 Guelma, Guelma, Algeria.
PLoS One. 2024 Jul 16;19(7):e0304575. doi: 10.1371/journal.pone.0304575. eCollection 2024.
In this research paper, we investigate the existence and uniqueness of solutions for neutral functional differential equations with sequential fractional orders, specifically involving the [Formula: see text]-Caputo operator. To obtain the desired results, we employ the Banach fixed point theorem (BFPT), a nonlinear variation of the Leray-Schauder fixed point theorem (SFPT), and the Krasnoselski fixed point theorem (KFPT). Additionally, we provide illustrative examples that demonstrate the key findings. Furthermore, we address a scenario where an initial value integral condition is considered.
在本研究论文中，我们研究了具有序分数阶的中立泛函微分方程解的存在性和唯一性，具体涉及到[Formula: see text]-Caputo 算子。为了得到所需的结果，我们使用了巴拿赫不动点定理（BFPT）、莱雷-斯卡尔德不动点定理（SFPT）的非线性变体以及克拉索尔斯基不动点定理（KFPT）。此外，我们提供了说明性的例子，以展示主要的发现。此外，我们还考虑了一个初始值积分条件的情况。
