A class of neutral fractional differential equations with  distributed delays and positive and negative coefficients are investigated. Using the Banach contraction mapping principle, by overcoming the operator construction and inequality scaling techniques, the sufficient conditions for the existence of bounded nonoscillatory solutions of the equations is obtained. Especially, the applicable range of these coefficients is extended to real numbers that are not equal to 1 and $-1$, the relevant results are verified by some examples.