On the oscillation of fractional differential equations

✍ Scribed by Said R. Grace; Ravi P. Agarwal; Patricia J.Y. Wong; Ağacık Zafer

• Book ID: 115064253
• Publisher: SP Versita
• Year: 2012
• Tongue: English
• Weight: 174 KB
• Volume: 15
• Category: Article
• ISSN: 1311-0454
• DOI: 10.2478/s13540-012-0016-1

✦ Synopsis

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 $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
aq 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.