  In this paper, we investigate stochastic partial differential equations
driven by multi-parameter anisotropic fractional Levy noises, including the
stochastic Poisson equation, the linear heat equation, and the quasi-linear
heat equation. Well-posedness of these equations under the fractional noises
will be addressed. The multi-parameter anisotropic fractional Levy noise is
defined as the formal derivative of the anisotropic fractional Levy random
field. In doing so, there are two folds involved. First, we consider the
anisotropic fractional Levy random field as the generalized functional of the
path of the pure jump Levy process. Second, we build} the Skorohod integration
with respect to the multi-parameter anisotropic fractional Levy noise by white
noise approach.
