On the oscillatory behavior of solutions of nonlinear fractional differential equations

The study of oscillation theory for fractional differential equations has been initiated by Grace et.al. [14] In this paper we establish some new criteria for the oscillation of fractional differential equations with the Caputo derivative of the form cD(a)(alpha)x(t) = e(t) + f(t,x(t)), a > 1, alpha is an element of(1,2) We also present the conditions under which all solutions of this equation are asymptotic to at + b as t -> infinity for some real numbers a, b. We shall employ a different technique rather than that in [14]. (C) 2015 Elsevier Inc. All tights reserved.