Philos-type oscillation criteria for impulsive fractional differential equations

In this paper, we study the oscillation of the impulsive Riemann-Liouville fractional differential equation {[r(t)D(tk+)(alpha)x(t)]' + q(t)f (d + integral(t)(tk+) (t - s)(-alpha) x(s)ds) = 0, t is an element of (t(k), t(k+1)], k = 0, 1, 2 ..., 1/d D(tk+)(alpha)x(t(k)(+)) - D(tk-1+)(alpha)x(t(k)(-))/d+integral(tk-)(tk-1+) (t(k)(-) - s)(-alpha) x(s)ds = -b(k), k = 1, 2, ... Philos-type oscillation criteria of the equation are obtained. We are interested in finding adequate impulsive controls to make the fractional system with Riemann-Liouville derivatives oscillate. An example of the change from non-oscillation to oscillation under the impulsive conditions is found.