Oscillation Behavior for a Class of Differential Equation with Fractional-Order Derivatives

Abstract EN

By using a generalized Riccati transformation technique and an inequality, we establish some oscillation theorems for the fractional differential equation [ a t p t + q t D - α x t ) γ ′ − b ( t ) f ∫ t ∞ ( s - t ) - α x ( s ) d s = 0 , for t ⩾ t 0 > 0 , where D - α x is the Liouville right-sided fractional derivative of order α ∈ ( 0,1 ) of x and γ is a quotient of odd positive integers.

The results in this paper extend and improve the results given in the literatures (Chen, 2012).