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We prove existence and uniqueness of solutions to a class of porous mediaequations driven by the fractional Laplacian when the initial data are positivefinite Radon measures on the Euclidean space. For given solutions without aprescribed initial condition, the problem of existence and uniqueness of theinitial trace is also addressed. By the same methods we can also treat weightedfractional porous media equations, with a weight that can be singular at theorigin, and must have a sufficiently slow decay at infinity (power-like). Inparticular, we show that the Barenblatt-type solutions exist and are unique.Such a result has a crucial role in [24], where the asymptotic behavior ofsolutions is investigated. Our uniqueness result solves a problem left open,even in the non-weighted case, in [42]

Fractional porous media equations: existence and uniqueness of weak solutions with measure data