On the oscillation of fractional-order delay differential equations with constant coefficients

• It is a well-recognized belief that fractional calculus leads to better results than classical calculus.
• We give oscillation criteria for the first order delay differential equation with fractional-order derivative.
• We give oscillation criteria for the second order delay differential equation with fractional-order derivative.
• We use alpha-exponential function which is a kind of functions that play the same role of the classical exponential functions.
• We use Laplace transformation formulations of fractional-order derivatives to obtain our results.

In this manuscript, some oscillation results are given including sufficient conditions or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients. For this, αα-exponential function which is a kind of functions that play the same role of the classical exponential functions and Laplace transformation formulations of fractional-order derivatives are used.