Oscillation Criteria for Higher Order Fractional Differential Equations with Mixed Nonlinearities

Abstract

In this article, we consider higher order fractional nonlinear differential equation of type \begin{align*} &_aD_t^qx(t)-p(t)x(t)+\sum_{i=1}^m q_i(t)|x(t)|^{\lambda_i-1}x(t)=v(t)\notag\\ &\underset{t\rightarrow a^+}{\lim}J_a^{n-q}x(t)=a_n\\ &_aD_t^{q-k}x(a)=a_k, \quad\quad\ k=1,...,n-1\notag \end{align*} where $_aD_t^q$is Riemann-Liouville fractional differential operator of order $q$, $m-1<q\leq m, m\geq1$ is an integer. We obtain some oscillation criteria for this equation.

Keywords

• fractional differential equations,Oscillation

References

1. [1] Shao, J., Zheng, Z. and Meng, F. Oscillation criteria for higher order fractional differential equations with mixed nonlinearities, Advanced in Difference Equations 2013:323 (2013)
2. [2] Chen,D. X., Qu, P. X. and Lan, Y. H., Forced oscillation of certain fractional differantial equations, Advanced in Difference Equations 2013:125 (2013)
3. [3] Grace, S. R., Agarwal, R. P., Wong, P. J.Y. and Zafer, A. On the oscillation of fractional differential equations, An International Journal for Theory and Applications Vol:15, No:2 (2012)
4. [4] Diethelm, K. The Analysis of Fractional Differential Equations, Springer, Berlin(2010)