On oscillatory and nonoscillatory behavior of solutions for a class of fractional order differential equations

Authors: ARJUMAND SEEMAB, MUJEEB UR REHMAN

Abstract: This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}u(t)+\lambda u(t)=f(t,u(t)),~~t> 0,$ $D^{\alpha-1}_{0}u(t)|_{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}u(t)=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1<\alpha\leq 2$ and $\lambda\in[1,\infty).$ Properties of the Mittag--Leffler function are utilized to establish our main results.

Keywords: Fractional differential equations, oscillation, asymptotic behavior, the Riemann-Liouville differential operator, the Mittag-Leffler function

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