Existence of nonoscillatory solutions for fractional neutral differential equations

In this paper, we present sufficient conditions for the existence of nonoscillatory solutions of the following fractional neutral functional differential equation Dtα[x(t)−cx(t−τ)]+∑i=1mPi(t)x(t−σi)=0,t≥t0,where Dtα is Liouville fractional derivatives of order α∈[1,+∞) on the half-axis, c, τ, σi∈(0,+∞), Pi∈C([t0,+∞),R), m≥1 is an integer.