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dc.contributor.authorAgarwal, Ravi
dc.contributor.authorHristova, Snezhana
dc.contributor.authorO’Regan, Donal
dc.date.accessioned2018-09-20T15:59:01Z
dc.date.available2018-09-20T15:59:01Z
dc.date.issued2015-11-06
dc.identifier.citationAgarwal, Ravi; Hristova, Snezhana; O’Regan, Donal (2015). Lyapunov functions and strict stability of caputo fractional differential equations. Advances in Difference Equations ,
dc.identifier.issn1687-1847
dc.identifier.urihttp://hdl.handle.net/10379/10131
dc.description.abstractOne of the main properties studied in the qualitative theory of differential equations is the stability of solutions. The stability of fractional order systems is quite recent. There are several approaches in the literature to study stability, one of which is the Lyapunov approach. However, the Lyapunov approach to fractional differential equations causes many difficulties. In this paper a new definition (based on the Caputo fractional Dini derivative) for the derivative of Lyapunov functions to study a nonlinear Caputo fractional differential equation is introduced. Comparison results using this definition and scalar fractional differential equations are presented, and sufficient conditions for strict stability and uniform strict stability are given. Examples are presented to illustrate the theory.
dc.publisherSpringer Nature
dc.relation.ispartofAdvances in Difference Equations
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Ireland
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/3.0/ie/
dc.subjectstrict stability
dc.subjectlyapunov functions
dc.subjectcaputo derivatives
dc.subjectfractional differential equations
dc.subjectorder systems
dc.subjecttheorem
dc.subjectdelay
dc.titleLyapunov functions and strict stability of caputo fractional differential equations
dc.typeArticle
dc.identifier.doi10.1186/s13662-015-0674-5
dc.local.publishedsourcehttps://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-015-0674-5
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 3.0 Ireland