  In the present paper we exhaustively examine the physical status of the
socalled Matese-Whitman mass function [J.J. Matese and P.G. Whitman, Phys. Rev.
D, 22, 1270 (1980)]. As a first step, we construct the relevant Einstein field
equations with an anisotropic matter distribution under the approach of
Conformal killing Vector. In the intermideate step we find a set of exact
solutions by using the Matese-Whitman mass function. Eventually we conduct
several physical tests to explore features of the applied mass function in
connection to the specific compact stars. It can be observed that all the
features of the model based on the Matese-Whitman mass function are of physical
interests.
