  A single Israel layer can be created when two metrics adjoin with no
continuous metric derivative across the boundary. The properties of the layer
depend only on the two metrics it separates. By using a fractional derivative
match, a family of Israel layers can be created between the same two metrics.
The family is indexed by the order of the fractional derivative. The method is
applied to Tolman IV and V interiors and a Schwarzschild vacuum exterior. The
method creates new ranges of modeling parameters for fluid spheres. A thin
shell analysis clarifies pressure/tension in the family of boundary layers.
