Fractional differential equations and Volterra–Stieltjes integral equations of the second kind

Detalhes bibliográficos
Autor(a) principal: Asanov, Avyt
Data de Publicação: 2019
Outros Autores: Almeida, Ricardo, Malinowska, Agnieszka B.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/26680
Resumo: In this paper, we construct a method to find approximate solutions to fractional differential equations involving fractional derivatives with respect to another function. The method is based on an equivalence relation between the fractional differential equation and the Volterra– Stieltjes integral equation of the second kind. The generalized midpoint rule is applied to solve numerically the integral equation and an estimation for the error is given. Results of numerical experiments demonstrate that satisfactory and reliable results could be obtained by the proposed method.
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spelling Fractional differential equations and Volterra–Stieltjes integral equations of the second kindFractional differential equationVolterra–Stieltjes integral equationGeneralized midpoint ruleIn this paper, we construct a method to find approximate solutions to fractional differential equations involving fractional derivatives with respect to another function. The method is based on an equivalence relation between the fractional differential equation and the Volterra– Stieltjes integral equation of the second kind. The generalized midpoint rule is applied to solve numerically the integral equation and an estimation for the error is given. Results of numerical experiments demonstrate that satisfactory and reliable results could be obtained by the proposed method.Springer2019-10-04T11:49:39Z2019-12-01T00:00:00Z2019-12info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/26680eng2238-360310.1007/s40314-019-0941-2Asanov, AvytAlmeida, RicardoMalinowska, Agnieszka B.info: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:RCAAP2024-02-22T11:51:40Zoai:ria.ua.pt:10773/26680Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:59:36.516511Repositório 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 Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
title Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
spellingShingle Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
Asanov, Avyt
Fractional differential equation
Volterra–Stieltjes integral equation
Generalized midpoint rule
title_short Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
title_full Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
title_fullStr Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
title_full_unstemmed Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
title_sort Fractional differential equations and Volterra–Stieltjes integral equations of the second kind
author Asanov, Avyt
author_facet Asanov, Avyt
Almeida, Ricardo
Malinowska, Agnieszka B.
author_role author
author2 Almeida, Ricardo
Malinowska, Agnieszka B.
author2_role author
author
dc.contributor.author.fl_str_mv Asanov, Avyt
Almeida, Ricardo
Malinowska, Agnieszka B.
dc.subject.por.fl_str_mv Fractional differential equation
Volterra–Stieltjes integral equation
Generalized midpoint rule
topic Fractional differential equation
Volterra–Stieltjes integral equation
Generalized midpoint rule
description In this paper, we construct a method to find approximate solutions to fractional differential equations involving fractional derivatives with respect to another function. The method is based on an equivalence relation between the fractional differential equation and the Volterra– Stieltjes integral equation of the second kind. The generalized midpoint rule is applied to solve numerically the integral equation and an estimation for the error is given. Results of numerical experiments demonstrate that satisfactory and reliable results could be obtained by the proposed method.
publishDate 2019
dc.date.none.fl_str_mv 2019-10-04T11:49:39Z
2019-12-01T00:00:00Z
2019-12
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/26680
url http://hdl.handle.net/10773/26680
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2238-3603
10.1007/s40314-019-0941-2
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.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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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