Oscillation theorems for fractional neutral differential equations

Authors : Yi-zhuo Wang, Zhen-lai Han, Ping Zhao, Shu-rong Sun

Pages : 1477-1488

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Publication Date : 2015-12-01

Article Type : Research

Abstract :In this paper we study the oscillation of the fractional neutral differential equation $$D^\alpha_t[a(t)D^\alpha(x(t)+p(t)x(\tau(t)))]+q(t)x(\sigma(t))=0,$$  where $D^\alpha_t$   is a modified Riemann-Liouville derivative. The obtained results are based on the new comparison theorems, which enable us to reduce the oscillatory problem of 2 α -order fractional differential equation to the oscillation of the first order equation. The results are easily verified. 
Keywords : Oscillation, fractional differential equation, modified Riemann-Liouville derivative, comparison theorem