Fractional derivatives of Colombeau generalized stochastic processes defined on R+

We consider Caputo and Riemann-Liouville fractional derivatives of a Colombeau generalized stochastic process $G$ defined on ${mathbb R}^+$. We give proper definitions and prove that both are Colombeau generalized stochastic processes themselves. We also give a solution to a certain Cauchy problem illustrating the application of the theory.