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In this article, we compute tables of values for the Riemann-Liouville
fractional derivative of the generalized polylogarithm functions considering parameter values µ = 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 µ = 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 R ∞
0
t
s−1e−3t
(1−ze−t)
3 ;
R ∞
0
t
s−1e−4t
(1−ze−t)
4 ;
R ∞
0
t
s−1e−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
Asifa Tassaddiq, Rana Alabdan. (2020) Computation of the Values for the Riemann-Liouville Fractional Derivative of the Generalized Poly-logarithm Functions, Punjab University Journal of Mathematics, Volume 52 , Issue No.3.
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