Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets
Autor(a) principal: | |
---|---|
Data de Publicação: | 2023 |
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/10773/38335 |
Resumo: | This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived by means of fractional Bernstein polynomials. The oscillation equation describes electrical circuits and exhibits a wide range of nonlinear dynamical behaviors. The proposed variable order model is of current interest in a lot of application areas in engineering and applied sciences. The purpose of this study is to analyze the behavior of the fractional force-free and forced oscillation equations under the variable-order fractional operator. The basic idea behind using the approximation technique is that it converts the proposed model into non-linear algebraic equations with the help of collocation nodes for easy computation. Different cases of the proposed model are examined under the selected variable order parameters for the first time in order to show the precision and performance of the mentioned scheme. The dynamic behavior and results are presented via tables and graphs to ensure the validity of the mentioned scheme. Further, the behavior of the obtained solutions for the variable order is also depicted. From the calculated results, it is observed that the mentioned scheme is extremely simple and efficient for examining the behavior of nonlinear random (constant or variable) order fractional models occurring in engineering and science. |
id |
RCAP_bb33c5a95acc3fd6ea821ae9e7002dcd |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/38335 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein waveletsFractional‐order Bernstein waveletsVariable‐order fractional oscillation equationsFunction approximationsError analysisCollocation gridThis article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived by means of fractional Bernstein polynomials. The oscillation equation describes electrical circuits and exhibits a wide range of nonlinear dynamical behaviors. The proposed variable order model is of current interest in a lot of application areas in engineering and applied sciences. The purpose of this study is to analyze the behavior of the fractional force-free and forced oscillation equations under the variable-order fractional operator. The basic idea behind using the approximation technique is that it converts the proposed model into non-linear algebraic equations with the help of collocation nodes for easy computation. Different cases of the proposed model are examined under the selected variable order parameters for the first time in order to show the precision and performance of the mentioned scheme. The dynamic behavior and results are presented via tables and graphs to ensure the validity of the mentioned scheme. Further, the behavior of the obtained solutions for the variable order is also depicted. From the calculated results, it is observed that the mentioned scheme is extremely simple and efficient for examining the behavior of nonlinear random (constant or variable) order fractional models occurring in engineering and science.MDPI2023-07-04T09:17:58Z2023-01-01T00:00:00Z2023info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/38335eng10.3390/math11112503Rayal, AshishJoshi, Bhagawati PrasadPandey, MukeshTorres, Delfim F. M.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:RCAAP2024-02-22T12:14:01Zoai:ria.ua.pt:10773/38335Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:08:27.667493Repositório 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 |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets |
title |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets |
spellingShingle |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets Rayal, Ashish Fractional‐order Bernstein wavelets Variable‐order fractional oscillation equations Function approximations Error analysis Collocation grid |
title_short |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets |
title_full |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets |
title_fullStr |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets |
title_full_unstemmed |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets |
title_sort |
Numerical Investigation of the fractional oscillation equations under the context of variable order caputo fractional derivative via fractional order Bernstein wavelets |
author |
Rayal, Ashish |
author_facet |
Rayal, Ashish Joshi, Bhagawati Prasad Pandey, Mukesh Torres, Delfim F. M. |
author_role |
author |
author2 |
Joshi, Bhagawati Prasad Pandey, Mukesh Torres, Delfim F. M. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Rayal, Ashish Joshi, Bhagawati Prasad Pandey, Mukesh Torres, Delfim F. M. |
dc.subject.por.fl_str_mv |
Fractional‐order Bernstein wavelets Variable‐order fractional oscillation equations Function approximations Error analysis Collocation grid |
topic |
Fractional‐order Bernstein wavelets Variable‐order fractional oscillation equations Function approximations Error analysis Collocation grid |
description |
This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived by means of fractional Bernstein polynomials. The oscillation equation describes electrical circuits and exhibits a wide range of nonlinear dynamical behaviors. The proposed variable order model is of current interest in a lot of application areas in engineering and applied sciences. The purpose of this study is to analyze the behavior of the fractional force-free and forced oscillation equations under the variable-order fractional operator. The basic idea behind using the approximation technique is that it converts the proposed model into non-linear algebraic equations with the help of collocation nodes for easy computation. Different cases of the proposed model are examined under the selected variable order parameters for the first time in order to show the precision and performance of the mentioned scheme. The dynamic behavior and results are presented via tables and graphs to ensure the validity of the mentioned scheme. Further, the behavior of the obtained solutions for the variable order is also depicted. From the calculated results, it is observed that the mentioned scheme is extremely simple and efficient for examining the behavior of nonlinear random (constant or variable) order fractional models occurring in engineering and science. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-04T09:17:58Z 2023-01-01T00:00:00Z 2023 |
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/10773/38335 |
url |
http://hdl.handle.net/10773/38335 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.3390/math11112503 |
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 |
|
_version_ |
1799137737115172864 |