Oscillation criteria for a class of fractional delay differential equations

Abstract

Abstract This paper is devoted to the oscillatory problem in the fractional-order delay differential equations. First, we prove the convergence of the Laplace transform of a fractional operator by the generalized Gronwall inequality with singularity and fractional calculus technique. Then we show that it exhibits oscillation dynamics if the corresponding characteristic equation has no real roots. We further provide other direct and effective criteria depending on the system parameters and fractional exponent. Finally, we carry out some numerical simulations to illustrate our results.

Keywords

• Oscillation
• Fractional differential equation
• Delay