Fractional Dynamics: A Comprehensive Exploration of Non-integer Order Systems

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Autor(es): dc.contributorFaculdade de Engenharia-
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.contributorUniversidade Tecnológica Federal do Paraná-
Autor(es): dc.contributorUniversidade Federal de Mato Grosso do Sul (UFMS)-
Autor(es): dc.creatorAbreu, Felipe Lima de-
Autor(es): dc.creatorFilipus, Murilo Cesar-
Autor(es): dc.creatorOliveira, Clivaldo de-
Autor(es): dc.creatorBalthazar, José Manoel-
Autor(es): dc.creatorRibeiro, Mauricio A.-
Autor(es): dc.creatorTusset, Angelo Marcelo-
Autor(es): dc.creatorVaranis, Marcus-
Data de aceite: dc.date.accessioned2025-08-21T22:21:09Z-
Data de disponibilização: dc.date.available2025-08-21T22:21:09Z-
Data de envio: dc.date.issued2025-04-29-
Data de envio: dc.date.issued2023-12-31-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.1590/1806-9126-RBEF-2024-0171-
Fonte completa do material: dc.identifierhttps://hdl.handle.net/11449/305188-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/305188-
Descrição: dc.descriptionThis article delves into the applications of fractional calculus, an extension of classical calculus that introduces non-integer derivative orders. The primary focus of this research is to present a methodology for simulating fractional differential equations and to explore the effects of fractional order in two well-known dynamic systems: the Van der Pol and Duffing systems. These systems are known for their nonlinear characteristics and, in certain cases, exhibit complex and rich dynamic behaviors. Initially, the Grunwald-Letnikov definition of fractional derivatives is introduced, followed by the general numerical solution for a fractional differential equation. The Van der Pol system is modified by the inclusion of a fractional time derivative of order q, reducing the integer order of the system to 1 + q, while the Duffing system is modified in terms of viscous damping, by the add of a fractional damping, which is now related to the fractional variation in displacement. The dynamics of the systems are characterized using classical methods of nonlinear dynamics, such as time-response, Poincaré sections, bifurcation diagrams and fast Fourier transform, as well as more advanced approaches, such as the continuous wavelet transform (CWT) and the Hilbert-Huang transform (HHT).-
Descrição: dc.descriptionUniversidade Federal da Grande Dourados Faculdade de Engenharia, MS-
Descrição: dc.descriptionUniversidade Estadual Paulista Departamento de Engenharia Elétrica, SP-
Descrição: dc.descriptionUniversidade Tecnológica Federal do Paraná, PR-
Descrição: dc.descriptionUniversidade Federal de Mato Grosso do Sul Instituto de Física, MS-
Descrição: dc.descriptionUniversidade Estadual Paulista Departamento de Engenharia Elétrica, SP-
Idioma: dc.languageen-
Relação: dc.relationRevista Brasileira de Ensino de Fisica-
???dc.source???: dc.sourceScopus-
Palavras-chave: dc.subjectFractional calculus-
Palavras-chave: dc.subjectNonlinear dynamics-
Palavras-chave: dc.subjectTime-frequency analysis-
Título: dc.titleFractional Dynamics: A Comprehensive Exploration of Non-integer Order Systems-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional - Unesp

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