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

Authors : Arjumand SEEMAB, Mujeeb Ur REHMAN

Pages : 1182-1194

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :This work aims to develop oscillation criterion and asymptotic behavior of solutions for a class of fractional order differential equation: $D^{\alpha}_{0}uinsert ignore into journalissuearticles values(t);+\lambda uinsert ignore into journalissuearticles values(t);=finsert ignore into journalissuearticles values(t,uinsert ignore into journalissuearticles values(t););,~~t> 0,$ $D^{\alpha-1}_{0}uinsert ignore into journalissuearticles values(t);|_{t=0}=u_{0},~~\lim_{t\to 0}J^{2-\alpha}_{0}uinsert ignore into journalissuearticles values(t);=u_{1}$ where $D^{\alpha}_{0}$ denotes the Riemann--Liouville differential operator of order $\alpha$ with $1
Keywords : Fractional differential equations, oscillation, asymptotic behavior, the Riemann Liouville differential operator, the Mittag Leffler function