Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/32623 |
Resumo: | The main aim of the paper is to present an algorithm to solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional fractional derivative on a finite interval. The main condition is connected with the one sided Lipschitz condition of the right hand side part of the given equation. An iterative scheme, based on appropriately defined mild lower and mild upper solutions, is provided. Two monotone sequences, increasing and decreasing ones, are constructed and their convergence to mild solutions of the given problem is established. In the case of uniqueness, both limits coincide with the unique solution of the given problem. The approximate method is based on the application of the method of lower and upper solutions combined with the monotone-iterative technique. |
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Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivativesRiemann–Liouville proportional fractional derivativeDifferential equationsImpulsesInitial value problemLower solutionsUpper solutionsMonotone-iterative techniqueThe main aim of the paper is to present an algorithm to solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional fractional derivative on a finite interval. The main condition is connected with the one sided Lipschitz condition of the right hand side part of the given equation. An iterative scheme, based on appropriately defined mild lower and mild upper solutions, is provided. Two monotone sequences, increasing and decreasing ones, are constructed and their convergence to mild solutions of the given problem is established. In the case of uniqueness, both limits coincide with the unique solution of the given problem. The approximate method is based on the application of the method of lower and upper solutions combined with the monotone-iterative technique.MDPI2021-11-19T18:59:39Z2021-08-02T00:00:00Z2021-08-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/32623eng10.3390/math9161979Agarwal, Ravi P.Hristova, SnezhanaO’Regan, DonalAlmeida, Ricardoinfo: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:RCAAP2024-02-22T12:02:41Zoai:ria.ua.pt:10773/32623Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:04:10.026931Repositório 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 |
Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives |
title |
Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives |
spellingShingle |
Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives Agarwal, Ravi P. Riemann–Liouville proportional fractional derivative Differential equations Impulses Initial value problem Lower solutions Upper solutions Monotone-iterative technique |
title_short |
Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives |
title_full |
Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives |
title_fullStr |
Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives |
title_full_unstemmed |
Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives |
title_sort |
Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives |
author |
Agarwal, Ravi P. |
author_facet |
Agarwal, Ravi P. Hristova, Snezhana O’Regan, Donal Almeida, Ricardo |
author_role |
author |
author2 |
Hristova, Snezhana O’Regan, Donal Almeida, Ricardo |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Agarwal, Ravi P. Hristova, Snezhana O’Regan, Donal Almeida, Ricardo |
dc.subject.por.fl_str_mv |
Riemann–Liouville proportional fractional derivative Differential equations Impulses Initial value problem Lower solutions Upper solutions Monotone-iterative technique |
topic |
Riemann–Liouville proportional fractional derivative Differential equations Impulses Initial value problem Lower solutions Upper solutions Monotone-iterative technique |
description |
The main aim of the paper is to present an algorithm to solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional fractional derivative on a finite interval. The main condition is connected with the one sided Lipschitz condition of the right hand side part of the given equation. An iterative scheme, based on appropriately defined mild lower and mild upper solutions, is provided. Two monotone sequences, increasing and decreasing ones, are constructed and their convergence to mild solutions of the given problem is established. In the case of uniqueness, both limits coincide with the unique solution of the given problem. The approximate method is based on the application of the method of lower and upper solutions combined with the monotone-iterative technique. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-11-19T18:59:39Z 2021-08-02T00:00:00Z 2021-08-02 |
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/10773/32623 |
url |
http://hdl.handle.net/10773/32623 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.3390/math9161979 |
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 |
MDPI |
publisher.none.fl_str_mv |
MDPI |
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 |
repository.mail.fl_str_mv |
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1799137697282916352 |