On the Oscillation of Three Dimensional Katugampola Fractional Delay Differential Systems

Abstract

In this study, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{eqnarray*} 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{eqnarray*} 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.