On oscillation of integro-differential equations

We study the oscillatory behavior of solutions for integro-differential equations of the form x'(t) = e(t) - integral(t)(0) (t - s)(alpha-1) k(t,s) f (s,x(s))ds, t >= 0 where 0 < alpha < 1. Our method is based on the use of the beta function and asymptotic behavior of nonoscillatory solutions. An example is given to illustrate the main result. Equations of this form include Caputo type fractional differential equations, so the results are applicable to some fractional type differential equations as well.