On the oscillation of fractional differential equations

Abstract

In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form Dqax+f1(t,x)=v(t)+f2(t,x),limt→aJ1−qax(t)=b1 , where D a q denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville differential operator is replaced by Caputo’s differential operator.