Determination of the Renewal Function of Some Renewal Processes

‎There is a one to one correspondence between renewal function and the probability density function of the times of observations of the successive occurrences of each renewal process‎. ‎Furthermore‎, ‎practical application of renewal processes requires renewal function information‎, ‎and this function plays an essential role in the study of renewal processes behavior by which predictions could be made‎. ‎In this paper‎, ‎the renewal functions corresponding with two distributions with the times of successive observations distributed by Erlang (n,lambda) ‎ , ‎and uniform (0,b)  are determined by Laplace transform and its theorems‎. ‎Finally‎, ‎an application of the renewal process is presented in physics‎.