On the oscillatory behavior of solutions of higher order nonlinear fractional differential equations

The study of oscillation theory for fractional differential equations has been initiated by Grace et al. [5]. In this paper we establish some new criteria for the oscillation of fractional differential equations with the Caputo derivative of the form (C)D(a)(r)x(t) = e(t) + f(t, x(t)), t > 0, a > 1, where r = alpha + n - 1, alpha is an element of(0, 1), and n - 1 is a natural number. We also present the conditions under which all solutions of this equation are asymptotic to t(n-1) as t -> infinity.