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 Paper

Abstract :In this paper we study the oscillation of the fractional neutral differential equation $$D^\alpha_t[ainsert ignore into journalissuearticles values(t);D^\alphainsert ignore into journalissuearticles values(xinsert ignore into journalissuearticles values(t);+pinsert ignore into journalissuearticles values(t);xinsert ignore into journalissuearticles values(\tauinsert ignore into journalissuearticles values(t);););]+qinsert ignore into journalissuearticles values(t);xinsert ignore into journalissuearticles values(\sigmainsert ignore into journalissuearticles values(t););=0,$$  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