On the Numerical Computation of the Mittag-Leffler Function

Detalhes bibliográficos
Autor(a) principal: Ortigueira, Manuel D.
Data de Publicação: 2019
Outros Autores: Lopes, António M., Tenreiro Machado, José
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/99790
Resumo: 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.
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spelling On the Numerical Computation of the Mittag-Leffler Functionfast Fourier transformMittag-Leffler functionnumerical computationStatistical and Nonlinear PhysicsComputational MechanicsModelling and SimulationEngineering (miscellaneous)Mechanics of MaterialsPhysics and Astronomy(all)Applied MathematicsThe 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.CTS - Centro de Tecnologia e SistemasDEE2010-B2 SistemasUNINOVA-Instituto de Desenvolvimento de Novas TecnologiasDEE - Departamento de Engenharia Electrotécnica e de ComputadoresRUNOrtigueira, Manuel D.Lopes, António M.Tenreiro Machado, José2022-02-13T01:30:55Z2019-102019-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/99790eng1565-1339PURE: 16922074https://doi.org/10.1515/ijnsns-2018-0358info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T04:46:32Zoai:run.unl.pt:10362/99790Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:39:14.897590Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the Numerical Computation of the Mittag-Leffler Function
title On the Numerical Computation of the Mittag-Leffler Function
spellingShingle On the Numerical Computation of the Mittag-Leffler Function
Ortigueira, Manuel D.
fast Fourier transform
Mittag-Leffler function
numerical computation
Statistical and Nonlinear Physics
Computational Mechanics
Modelling and Simulation
Engineering (miscellaneous)
Mechanics of Materials
Physics and Astronomy(all)
Applied Mathematics
title_short On the Numerical Computation of the Mittag-Leffler Function
title_full On the Numerical Computation of the Mittag-Leffler Function
title_fullStr On the Numerical Computation of the Mittag-Leffler Function
title_full_unstemmed On the Numerical Computation of the Mittag-Leffler Function
title_sort On the Numerical Computation of the Mittag-Leffler Function
author Ortigueira, Manuel D.
author_facet Ortigueira, Manuel D.
Lopes, António M.
Tenreiro Machado, José
author_role author
author2 Lopes, António M.
Tenreiro Machado, José
author2_role author
author
dc.contributor.none.fl_str_mv CTS - Centro de Tecnologia e Sistemas
DEE2010-B2 Sistemas
UNINOVA-Instituto de Desenvolvimento de Novas Tecnologias
DEE - Departamento de Engenharia Electrotécnica e de Computadores
RUN
dc.contributor.author.fl_str_mv Ortigueira, Manuel D.
Lopes, António M.
Tenreiro Machado, José
dc.subject.por.fl_str_mv fast Fourier transform
Mittag-Leffler function
numerical computation
Statistical and Nonlinear Physics
Computational Mechanics
Modelling and Simulation
Engineering (miscellaneous)
Mechanics of Materials
Physics and Astronomy(all)
Applied Mathematics
topic fast Fourier transform
Mittag-Leffler function
numerical computation
Statistical and Nonlinear Physics
Computational Mechanics
Modelling and Simulation
Engineering (miscellaneous)
Mechanics of Materials
Physics and Astronomy(all)
Applied Mathematics
description 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.
publishDate 2019
dc.date.none.fl_str_mv 2019-10
2019-10-01T00:00:00Z
2022-02-13T01:30:55Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/99790
url http://hdl.handle.net/10362/99790
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1565-1339
PURE: 16922074
https://doi.org/10.1515/ijnsns-2018-0358
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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