Please use this identifier to cite or link to this item:
Title: Caputo fractional differential equation with state dependent delay and practical stability
Author: Agarwal, Ravi
Almeida, Ricardo
Hristova, Snezhana
O'Regan, Donal
Keywords: Functional-differential equations with fractional derivatives
Lyapunov functions
State dependent delay
Issue Date: 2019
Publisher: Dynamic Publishers, Inc
Abstract: Practical stability properties of Caputo fractional delay differential equations is studied and, in particular, the case with state dependent delays is considered. These type of delays is a generalization of several types of delays such as constant delays, time variable delays, or distributed delays. In connection with the presence of a delay in a fractional differential equation and the application of the fractional generalization of the Razumikhin method, we give a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. Three types of derivatives for Lyapunov functions, the Caputo fractional derivative, the Dini fractional derivative, and the Caputo fractional Dini derivative, are applied to obtain several sufficient conditions for practical stability. An appropriate Razumikhin condition is applied. These derivatives allow the application of non-quadratic Lyapunov function for studying stability properties. We illustrate our theory on several nonlinear Caputo fractional differential equations with different types of delays
Peer review: yes
DOI: 10.12732/dsa.v28i3.11
ISSN: 1056-2176
Publisher Version:
Appears in Collections:CIDMA - Artigos
SCG - Artigos

Formato BibTex MendeleyEndnote Degois 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.