We investigate optical superregular breathers in the femtosecond regime under dispersion management in an inho-mogeneous fiber goveed by the nonautonomous higher-order nonlinear Schr?dinger equation (NLSE). Exact solutions describing the dynamics of superregular breathers are obtained. Furthermore, we discuss the propagation behaviors of controllable superregular breathers, including stabilization and recurrence in an exponential dispersion fiber and a peri-odic distributed fiber system. Particularly, the nonlinear dynamics of superregular modes evolved from an identical initial small-amplitude modulation is analyzed in detail.