Electron. J. Differential Equations, Vol. 2019 (2019), No. 33, pp. 1-15.

Oscillatory and asymptotic properties of fractional delay differential equations

Jan Cermak, Tomas Kisela

Abstract:
This article discusses the oscillatory and asymptotic properties of a test delay differential system involving a non-integer derivative order. We formulate corresponding criteria via explicit necessary and sufficient conditions that enable direct comparisons with the results known for classical integer-order delay differential equations. In particular, we shall observe that oscillatory behaviour of solutions of delay system with non-integer derivatives embodies quite different features compared to the classical results known from the integer-order case.

Submitted March 20, 2018. Published February 22, 2019.
Math Subject Classifications: 34K37, 34A08, 34K11, 34K20.
Key Words: Fractional delay differential equation; oscillation; asymptotic behaviour.

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Jan Cermak
Institute of Mathematics
Brno University of Technology
Technicka 2
616 69 Brno, Czech Republic
email: cermak.j@fme.vutbr.cz
Tomas Kisela
Institute of Mathematics
Brno University of Technology
Technicka 2
616 69 Brno, Czech Republic
email: kisela@fme.vutbr.cz

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