Rotational periodic solutions for fractional iterative systems

• Main Authors: Rui Wu, Yi Cheng, Ravi P. Agarwal
• Format: Article
• Language: English
• Published: AIMS Press 2021-08-01
• Series: AIMS Mathematics
• Subjects: existence; rotational periodic; fractional iterative systems; neural network
• Online Access: https://www.aimspress.com/article/doi/10.3934/math.2021651?viewType=HTML

In this paper, we devoted to deal with the rotational periodic problem of some fractional iterative systems in the sense of Caputo fractional derivative. Under one sided-Lipschtiz condition on nonlinear term, the existence and uniqueness of solution for a fractional iterative equation is proved by applying the Leray-Schauder fixed point theorem and topological degree theory. Furthermore, the well posedness for a nonlinear control system with iteration term and a multivalued disturbance is established by using set-valued theory. The existence of solutions for a iterative neural network system is demonstrated at the end.