This paper presents some results obtained in PhD thesis entitled "A contribution to the analysis of integral characteristics of received signal envelope in wireless communications". For analytical and numerical evaluation of system performance, the probability density functions (pdf) describing the statistical behavior of the multipath fading envelope, are analyzed like particular solutions of corresponding differential equation, while the existence of singular solution is considered and analyzed under different conditions. It is shown that the envelope of probability density function curves family is a straight line, for all values of varying parameters, for Rayleigh, Weibull and Nakagami fading channel model. This new expression can be used during mobile system designing.