  The generalized Taylor's Formula is used to derive a fractional
radial-cylindrical diffusivity model via a fractional conservation of mass in
radial geometry in a petroleum reservoir. The result is a space-fractional
generalization of the diffusivity model with an arbitrary order that explains
the degree of heterogeneity of the medium (a continuous spectrum of zero to one
where zero heterogeneity equates to homogeneity). An implicit unconditionally
stable numerical difference scheme of the linear form of the derived model is
used to illustrate deviations of the model from the homogeneous medium. The
variation of the order produces additional localized pressure drops during flow
which is congruous with fluid inhibition effect of heterogeneity..
