Oscillation theorems for fractional neutral differential equations

Year 2015, Volume: 44 Issue: 6, 1477 - 1488, 01.12.2015

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

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 2α-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

References

• .