TY - JOUR
T1 - On the Numerical Computation of the Mittag-Leffler Function
AU - Ortigueira, Manuel D.
AU - Lopes, António M.
AU - Tenreiro Machado, José
N1 - info:eu-repo/grantAgreement/FCT/5876/147324/PT#
PY - 2019/10
Y1 - 2019/10
N2 - The Mittag-Leffler function (MLF) plays an important role in many applications of fractional calculus, establishing a connection between exponential and power law behaviors that characterize integer and fractional order phenomena, respectively. Nevertheless, the numerical computation of the MLF poses problems both of accuracy and convergence. In this paper, we study the calculation of the 2-parameter MLF by using polynomial computation and integral formulas. For the particular cases having Laplace transform (LT) the method relies on the inversion of the LT using the fast Fourier transform. Experiments with two other available methods compare also the computational time and accuracy. The 3-parameter MLF and its calculation are also considered.
AB - The Mittag-Leffler function (MLF) plays an important role in many applications of fractional calculus, establishing a connection between exponential and power law behaviors that characterize integer and fractional order phenomena, respectively. Nevertheless, the numerical computation of the MLF poses problems both of accuracy and convergence. In this paper, we study the calculation of the 2-parameter MLF by using polynomial computation and integral formulas. For the particular cases having Laplace transform (LT) the method relies on the inversion of the LT using the fast Fourier transform. Experiments with two other available methods compare also the computational time and accuracy. The 3-parameter MLF and its calculation are also considered.
KW - fast Fourier transform
KW - Mittag-Leffler function
KW - numerical computation
UR - http://www.scopus.com/inward/record.url?scp=85069637704&partnerID=8YFLogxK
U2 - 10.1515/ijnsns-2018-0358
DO - 10.1515/ijnsns-2018-0358
M3 - Article
AN - SCOPUS:85069637704
SN - 1565-1339
VL - 20
SP - 725
EP - 736
JO - International Journal of Nonlinear Sciences and Numerical Simulation
JF - International Journal of Nonlinear Sciences and Numerical Simulation
IS - 6
ER -