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
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].