- Turkish Journal of Mathematics
- Vol: 43 Issue: 3
- On oscillatory and nonoscillatory behavior of solutions for a class of fractional order differential...
On oscillatory and nonoscillatory behavior of solutions for a class of fractional order differential equations
Authors : Arjumand Seemab, Mujeeb Ur Rehman
Pages : 1182-1194
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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 $1Keywords : Fractional differential equations, oscillation, asymptotic behavior, the Riemann-Liouville differential operator, the Mittag-Leffler function