In this chapter, the dynamics of a particular topology of Colpitts oscillator with fractional order dynamics is presented. The first part is devoted to the dynamics of the model using standard nonlinear analysis techniques including time series, bifurcation diagrams, phase space trajectories plots, and Lyapunov exponents. One of the major results of this innovative work is the numerical finding of a parameter region in which the fractional order Colpitts oscillator's circuit experiences multiple attractors' behavior. This phenomenon was not reported previously in the Colpitts circuit (despite the huge amount of related research works) and thus represents an enriching contribution to the understanding of the dynamics of Chua's oscillator. The second part of this chapter deals with the synchronization of fractional order system. Based on fractional-order Lyapunov stability theory, this chapter provides a novel method to achieve generalized and phase synchronization of two and network fractional-order chaotic Colpitts oscillators, respectively.