Abstract
In this article, we compute tables of values for the Riemann-Liouville fractional derivative of the generalized polylogarithm functions considering parameter values mu = 3; 4; 5 and s = 1/2; 3/2; 1/2; 3/2. Several authors investigated such functions and their analytic properties, but no work can be found in the literature for the computation of their values. We perform numerical computations to evaluate Riemann-Liouville fractional derivative of the generalized polylogarithm functions for different values of the involved parameters. We validate the data obtained by using our new mathematical model (given in the form of a difference equation) and the known classical integral representations for mu = 3; 4; 5 and s = 1/2; 3/2. It is worth mentioning that for the positive values of parameter s = 1/2; 3/2, our calculations are consistent with the directly computed results by using their integral representation and 100% accuracy is achieved. Furthermore, it is obvious that the involved integrals integral(infinity)(0) t(s-1)e(-3)t/(1-ze(-t))(3); integral(infinity)(0) t(s-1)e(-4t)/(1-ze(-t))(4); integral(infinity)(0) t(s-1)e(-5t)/(1-ze(-t))(5); are not convergent for the negative values of parameter s and in this investigation we evaluate these integrals for the negative values of s.