Oscillation criteria for a certain class of fractional order integro-differential equations

Authors : Serkan ASLIYÜCE, A. Feza GÜVENİLİR, Ağacık ZAFER

Pages : 199-207

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Publication Date : 2017-04-01

Article Type : Research Paper

Abstract :In this paper, we shall give some new results about the oscillatory behavior of nonlinear fractional order integro-differential equations with forcing term $vinsert ignore into journalissuearticles values(t);$ of form \[ D_a^\alpha xinsert ignore into journalissuearticles values(t);=vinsert ignore into journalissuearticles values(t);-\int\limits_a^t Kinsert ignore into journalissuearticles values(t,s); Finsert ignore into journalissuearticles values(s,xinsert ignore into journalissuearticles values(s););ds, \,\, 0<\alpha <1,\,\, \lim\limits_{t\to a^+} J_a^{1-\alpha} xinsert ignore into journalissuearticles values(t);=b_1, \] where $v$, $K$ and $F$ are continuous functions, $b_1\in\mathbb{R}$, and $D_a^\alpha$ and $J_a^{1-\alpha}$ denote the Riemann-Liouville fractional order differential and integral operators respectively.
Keywords : fractional integro differential equations, oscillation, Riemann Liouville fractional operators, Caputo fractional derivative