Preprint Article Version 1 This version is not peer-reviewed

# Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems

Version 1 : Received: 18 October 2018 / Approved: 18 October 2018 / Online: 18 October 2018 (11:14:42 CEST)

A peer-reviewed article of this Preprint also exists.

Kilicman, A.; Sadhasivam, V.; Deepa, M.; Nagajothi, N. Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems. Symmetry 2018, 10, 769. Kilicman, A.; Sadhasivam, V.; Deepa, M.; Nagajothi, N. Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems. Symmetry 2018, 10, 769.

Journal reference: Symmetry 2018, 10, 769
DOI: 10.3390/sym10120769

## Abstract

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

## Subject Areas

oscillation; nonlinear differential system; delay differential system; α-fractional derivative