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

Abstract

In this paper, we shall give some new results about the oscillatory behavior of nonlinear fractional order integro-differential equations with forcing term $v(t)$ of form \[ D_a^\alpha x(t)=v(t)-\int\limits_a^t K(t,s) F(s,x(s))ds, \,\, 0<\alpha <1,\,\, \lim\limits_{t\to a^+} J_a^{1-\alpha} x(t)=b_1, \]

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

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