Fractional differential equations with a constant delay: Stability and asymptotics of solutions

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• 作者：Jan Čermá ; k ; ^a ; ^{cermak.j@fme.vutbr.cz} ; Zuzana Do&scaron ; lá ; ^b ; ^{dosla@math.muni.cz} ; Tomá ; &scaron ; Kisela^a ; ^{kisela@fme.vutbr.cz}
• 关键词：Delay differential equation ; Fractional-order derivative ; Stability ; Asymptotic behaviour
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：298
• 期：Complete
• 页码：336-350
• 全文大小：647 K
• 卷排序：298

文摘

The paper discusses stability and asymptotic properties of a fractional-order differential equation involving both delayed as well as non-delayed terms. As the main results, explicit necessary and sufficient conditions guaranteeing asymptotic stability of the zero solution are presented, including asymptotic formulae for all solutions. The studied equation represents a basic test equation for numerical analysis of delay differential equations of fractional type. Therefore, the knowledge of optimal stability conditions is crucial, among others, for numerical stability investigations of such equations. Theoretical conclusions are supported by comments and comparisons distinguishing behaviour of a fractional-order delay equation from its integer-order pattern.