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\in(0,1)}, and {n\geq 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\to\infty}.