The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a continuous distribution of bosons, characterized by a special form of the spectral density, is evaluated analytically. The special reservoir is designed to induce anomalous decoherence, resulting in an inverse power law relaxation, of power 3/2, over an evaluated long time scale. If compared to the exponential-like relaxation obtained from the original Jaynes-Cummings model for Lorentzian-type spectral density

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... , decoherence is strongly suppressed. The special reservoir exhibits an upper band edge frequency coinciding with the qubit transition frequency. Known theoretical models of photonic band gap media suitable for the realization of the designed reservoir are proposed.