On stability of delayed differential systems of arbitrary non-integer order
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This paper summarizes and extends known results on qualitative behaviorof solutions of autonomous fractional differential systems with a time delay. Itutilizes two most common definitions of fractional derivative, Riemann–Liouvilleand Caputo one, for which optimal stability conditions are formulated via positionof eigenvalues in the complex plane. Our approach covers differential systems ofany non-integer orders of the derivative. The differences in stability and asymptoticproperties of solutions induced by the type of derivative are pointed out as well.
Keywordsfractional delay differential system, stability, asymptotic behavior, Riemann–Liouville derivative, Caputo derivative
Document typePeer reviewed
Document versionFinal PDF
SourceMathematics for Applications. 2020 vol. 9, č. 1, s. 31-42. ISSN 1805-3629
- 2020/1