, Volume 15, Issue 2, pp 222-231
Date: 18 Mar 2012

On the oscillation of fractional differential equations

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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 $D_a^q x + f_1 (t,x) = v(t) + f_2 (t,x),\mathop {\lim }\limits_{t \to a} J_a^{1 - q} x(t) = b_1 $ , 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.