I explore a possibility to model AXPs and SGRs in terms of an isolated, young and relatively light neutron star accreting material from a fossil disk formed by the supernova ejecta fall-back. I show that the properties of these objects in X-rays can be explained within this accretion scenario provided the fossil disk is magnetized and non-Keplerian. The magnetic field strength of the neutron stars in this case lies in the interval 0.1-10 TG. The activity of SGRs in gamma-rays within this model can be associated with occasional nuclear explosions powered by fission of heavy nuclei in the crust of the young neutron star. The explosion can be triggered by instabilities of the boundary layer at the bottom of the accretion column.

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