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^α\left(u(t)\right)&=&p(t)g\left(v(σ(t))\right),\\ D^α\left(v(t)\right)&=&-q(t)h\left(w(t))\right),\\ D^α\left(w(t)\right)&=& r(t)f\left(u(τ(t))\right),~ t \geq t_0, \end{eqnarray*} where $0<\alpha \le 1$, $D^{\alpha }$ 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.

20 pages

References in corpus (2)

• A New Fractional Derivative with Classical Properties
• Variational Calculus with Conformable Fractional Derivatives