dc.contributor.author Agarwal, Ravi dc.contributor.author Hristova, Snezhana dc.contributor.author O’Regan, Donal dc.date.accessioned 2018-09-20T15:59:01Z dc.date.available 2018-09-20T15:59:01Z dc.date.issued 2015-11-06 dc.identifier.citation Agarwal, Ravi; Hristova, Snezhana; O’Regan, Donal (2015). Lyapunov functions and strict stability of caputo fractional differential equations. Advances in Difference Equations , dc.identifier.issn 1687-1847 dc.identifier.uri http://hdl.handle.net/10379/10131 dc.description.abstract One 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.publisher Springer Nature dc.relation.ispartof Advances in Difference Equations dc.rights Attribution-NonCommercial-NoDerivs 3.0 Ireland dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/3.0/ie/ dc.subject strict stability dc.subject lyapunov functions dc.subject caputo derivatives dc.subject fractional differential equations dc.subject order systems dc.subject theorem dc.subject delay dc.title Lyapunov functions and strict stability of caputo fractional differential equations dc.type Article dc.identifier.doi 10.1186/s13662-015-0674-5 dc.local.publishedsource https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-015-0674-5 nui.item.downloads 0
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