Some New Oscillation Criteria for a Class of Nonlinear Fractional Differential Equations with Damping Term

Several oscillation criteria are established for nonlinear fractional differential equations of the form{ a(t) [( r(t)g ( D−x(t) ))′]η}′ −F(t,∫ ∞ t (v− t)−αx(v)dv ) = 0, where D−x(t) is the Liouville right-side fractional derivative of order α ∈ (0,1) of x(t),η = 2n+1 2m+1 , and n,m∈N . F(t,G)∈C([t0,∞)×R;R) , and there exists function q(t)∈ C([t0,∞);R+) such that F(t,G) Gη q(t) for G = 0 and x = 0, t t0. We also give some examples to illustrate the main results.