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Strict stability with respect to initial time difference for Caputo fractional differential equations by Lyapunov functions

Strict stability with respect to initial time difference for Caputo fractional differential... Abstract The strict stability properties are generalized to nonlinear Caputo fractional differential equations in the case when both initial points and initial times are changeable. Using Lyapunov functions, some criteria for strict stability, eventually strict stability and strict practical stability are obtained. A brief overview of different types of derivatives in the literature related to the application of Lyapunov functions to Caputo fractional equations are given, and their advantages and disadvantages are discussed with several examples. The Caputo fractional Dini derivative with respect to to initial time difference is used to obtain some sufficient conditions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Strict stability with respect to initial time difference for Caputo fractional differential equations by Lyapunov functions

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References (17)

Publisher
de Gruyter
Copyright
Copyright © 2017 by the
ISSN
1072-947X
eISSN
1572-9176
DOI
10.1515/gmj-2016-0080
Publisher site
See Article on Publisher Site

Abstract

Abstract The strict stability properties are generalized to nonlinear Caputo fractional differential equations in the case when both initial points and initial times are changeable. Using Lyapunov functions, some criteria for strict stability, eventually strict stability and strict practical stability are obtained. A brief overview of different types of derivatives in the literature related to the application of Lyapunov functions to Caputo fractional equations are given, and their advantages and disadvantages are discussed with several examples. The Caputo fractional Dini derivative with respect to to initial time difference is used to obtain some sufficient conditions.

Journal

Georgian Mathematical Journalde Gruyter

Published: Mar 1, 2017

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