Generalized Proportional Caputo Fractional Differential Equations with Delay and Practical Stability by the Razumikhin Method

被引：2

作者：

Agarwal, Ravi ^{[1
]}

Hristova, Snezhana ^{[2
]}

O'Regan, Donal ^{[3
]}

机构：

[1] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX 78363 USA

[2] Univ Plovdiv Paisii Hilendarski, Fac Math & Informat, Plovdiv 4000, Bulgaria

[3] Natl Univ Ireland, Sch Math & Stat Sci, Galway H91 TK33, Ireland

来源：

MATHEMATICS | 2022年 / 10卷 / 11期

关键词：

generalized proportional Caputo fractional derivative; differential equations; bounded delays; practical stability; Lyapunov functions; Razumikhin type conditions; SYSTEMS;

D O I：

10.3390/math10111849

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Practical stability properties of generalized proportional Caputo fractional differential equations with bounded delay are studied in this paper. Two types of stability, practical stability and exponential practical stability, are defined and considered, and also some sufficient conditions to guarantee stability are presented. The study is based on the application of Lyapunov like functions and their generalized proportional Caputo fractional derivatives among solutions of the studied system where appropriate Razumikhin like conditions are applied (appropriately modified in connection with the fractional derivative considered). The theory is illustrated with several nonlinear examples.

引用

页数：15

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