Necessary and Sufficient Conditions for Existence and Uniqueness of Solutions to Nabla Fractional Systems

被引：1

作者：

Yang, Jikai ^{[1
]}

Li, Hongli ^{[1
]}

Zhang, Long ^{[1
]}

机构：

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China

来源：

FRACTAL AND FRACTIONAL | 2022年 / 6卷 / 12期

基金：

中国国家自然科学基金;

关键词：

nabla fractional systems; invertible function; proof by contradiction; existence and uniqueness; SYNCHRONIZATION;

D O I：

10.3390/fractalfract6120723

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the existence and uniqueness of solutions for nabla fractional systems. By using the properties of bijective functions, we obtain a necessary and sufficient condition ensuring the existence and uniqueness of solutions for a class of fractional discrete systems. Furthermore, we derive two sufficient conditions guaranteeing the existence of solutions by means of a nonlinear functional analysis method. In addition, the above conclusions are extended to high-dimensional delayed systems. Finally, two examples are given to illustrate the validity of our results.

引用

页数：12

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