Rotational periodic solutions for fractional iterative systems

Rui Wu; Yi Cheng; Ravi P. Agarwal; Rui Wu; Yi Cheng; Ravi P. Agarwal

doi:10.3934/math.2021651

AIMS Mathematics

2021, Volume 6, Issue 10: 11233-11245. doi: 10.3934/math.2021651

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Rotational periodic solutions for fractional iterative systems

1.
Department of Mathematics, Changchun University of Finance and Economics, Changchun 130122, China
2.
Department of Mathematical Sciences, Bohai University, Jinzhou 121013, China
3.
Department of Mathematics, Texas A & M University-Kingsville, Kingsville, Texas, USA

Received: 01 June 2021 Accepted: 26 July 2021 Published: 04 August 2021
MSC : 34C25, 34B16, 37J40

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.
- existence,
- rotational periodic,
- fractional iterative systems,
- neural network
Citation: Rui Wu, Yi Cheng, Ravi P. Agarwal. Rotational periodic solutions for fractional iterative systems[J]. AIMS Mathematics, 2021, 6(10): 11233-11245. doi: 10.3934/math.2021651

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Abstract

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.

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