The resonant behavior of a fractional linear oscillator subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise is considered. Using Laplace transformation technique and Shapiro-Loginov formula, exact expressions of the first moment for the system response and its long-time amplitude are presented. The influence of the system parameters on the long-time behavior of the system response is discussed, such as fractional order, friction coefficient, driving frequency, noise intensity and relevant rate. It is found that the long-time amplitude of the fractional oscillator behaves non-monotonical, that is, there exist stochastic resonances in a wide sense. Moreover, generalized stochastic resonance with two peaks can be found subject to some appropriate parameters.