Oscillatory and asymptotic properties of fractional delay differential equations

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.