Affiliation:
1. Dipartimento di Matematica e Fisica Università “Roma Tre” 1, Largo S. Leonardo Murialdo 00146 Rome, ITALY
Abstract
Abstract
Some analytical properties of the Mittag-Leffler functions,
e
α
(
t
)
≢
E
α
(
-
t
α
)
, are established on some t-intervals. These are lower and upper bounds obtained in terms of simple rational functions (which are related to the Padé approximants of
e
α
(
t
)
)
for
t
>
0
and
0
<
α
<
1.
. A new method, to compute such functions, solving numerically a Caputo-type fractional differential equation satisfied by them, is developed. This approach consists in an adaptive predictor-corrector method, based on the K. Diethelm's predictor-corrector algorithm, and is shown to outperform the current methods implemented by MATLAB® and by Mathematica when
t
is real and even possibly large
Subject
Applied Mathematics,Analysis
Cited by
19 articles.
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