Abstract
In this paper, we develop sufficient criteria for the existence of a nonoscillatory solution to the fractional neutral functional differential equation of the form: where Da t is Liouville fractional derivatives of order a = 0 on the half-axis, c. R, t, si. R +, Pi. C([ t0,8), R), Fi. C(R, R), i = 1, 2,..., m, m = 1 is an integer. Our results are new and improve many known results on the integer-order functional differential equations.