Numerical implementation of Mittag-Leffler function: a revision study
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References
1、DIETHELM, K. et al. Algorithms for the fractional calculus: a selection of numerical methods.
Computer methods in applied mechanics and engineering, Amsterdam, v. 194, n. 6-8, p.
743–773, 2005.
2、GORENFLO, R.; LOUTCHKO, J.; LUCHKO, Y. Computation of the mittag-leffler function
, (). Fractional Calculus and Applied Analysis, New York, v. 5, p. 491–518, 2002.
3、HAUBOLD, H. J.; MATHAI, A. M.; SAXENA, R. K. Mittag-leffler functions and their applications.
Journal of Applied Mathematics, Hindawi, v. 2011, p. 1–51, 2011.
4、HERRMANN, R. Fractional calculus: an introduction for physicists. [S.l.]: World Scientific,
2011.
5、MAGIN, R. et al. On the fractional signals and systems. Signal Processing, Amsterdam, v. 91, n. 3,
p. 350–371, 2011.
6、MITTAG-LEFFLER, G. Une généralisation de l’intégrale de laplace-abel. Comptes rendus de
l’Académie des Sciences, Paris, v. 137, p. 537–539, 1903.
7、MITTAG-LEFFLER, G. Sur la representation analytique d’une branche uniforme d’une fonction
monogene. Acta mathematica, Paris, v. 29, n. 1, p. 101–181, 1905.
8、MITTAG-LEFFLER, G. M. Sur la nouvelle fonction e (x). Comptes rendus de l’Académie des
Sciences, v. 137, n. 2, p. 554–558, 1903.
OLDHAM, K.; SPANIER, J. The fractional calculus: theory and applications of differentiation
and integration to arbitrary order. New York: [s.n.], 1974.
9、PODLUBNY, I. Fractional differential equations. Mathematics in science and engineering,
Amsterdam, v. 198, p. 41–119, 1999.
10、WIMAN, A. Über den fundamentalsatz in der teorie der funktionen (). Acta Mathematica,
Berlin, v. 29, p. 191–201, 1905.
11、CORREA, E. A.; CARDOSO, L. X.; TOGNETTI, T. C.; AMORIM, R. G. G. Numerical implementation of Mittag-Leffler function: a revision study.
C.Q.D. – Revista Eletrônica Paulista de Matemática, Bauru, v. 22, n. 2, p. 39–47, set. 2022. Edição Brazilian Symposium on Fractional Calculus.
DOI: 10.21167/cqdv22n22022039047 Disponível em: www.fc.unesp.br/departamentos/matematica/revista-cqd