Existence and Asymptotic Estimates of the Maximal and Minimal Solutions for a Coupled Tempered Fractional Differential System with Different Orders

Peng Chen,Xinguang Zhang, Lishuang Li,Yongsheng Jiang,Yonghong Wu

Axioms（2025）

School of Mathematical and Informational Sciences | School of Statistics and Mathematics | Department of Mathematics and Statistics

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Abstract

In this paper, we focus on the existence and asymptotic estimates of the maximal and minimal solutions for a coupled tempered fractional differential system with different orders. By introducing an order reduction technique and some new growth conditions, we establish some new results on the existence of positive extremal solutions for the tempered fractional differential system, meanwhile, we also obtain the asymptotic estimate of the positive extreme solution by an iterative technique, which possesses a sharp asymptotic estimate. In particular, the iterative sequences converging to maximal and minimal solutions starting from two known initial values are easy to compute. Moreover, the weight function ℏi is allowed to have an infinite number of singular points in [0,1].

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existence and asymptotic estimates,three-point boundary value problem,maximal and minimal solutions,iterative technique,reducing order technique

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【要点】：本文研究了具有不同阶数的耦合温阶分数微分系统的最大值和最小值解的存在性和渐近估计，提出了一种新的阶数降低技术和增长条件，得到了正极值解存在的新结果，并通过迭代技术获得了正极值解的锐利渐近估计。

【方法】：作者通过引入阶数降低技术和一些新的增长条件，建立了温阶分数微分系统正极值解存在性的新结果，同时使用迭代技术得到了正极值解的渐近估计。

【实验】：文中未提供具体的实验过程或使用的数据集名称，因此无法描述实验过程和结果。