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The build-up dynamics of a continuous spectrum under the action of a weak laser field on a Fano resonance with the use of the pulses with the Lorentz spectrum and ultrashort pulses in the wavelet form is investigated. A dispersion-time excitation dependence of the Fano resonances in a He atom, in an InP impurity semiconductor, in longitudinal optical LO-phonons of a shallow donor exciton in pure ZnO crystals, and in metamaterials are calculated. The numerical simulation of the dynamics has shown time-dependent formation a Fano spectral profile in the systems of different physical natures under the action of ultrashort pulses with attosecond and femtosecond durations.