Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/238330
Type: Artigo
Title: Solução da equação de Bessel via cálculo fracionário
Title Alternative: Solution of the Bessel equation via fractional calculus
Author: Rodrigues, Fabio G.
Oliveira, Edmundo C. de
Abstract: In this work we discuss the solvability of Bessel's differential equation of order p, which is a particular case of the confluent hypergeometric equation, from the perspective of the theory of calculus of arbitrary order, also usually known as fractional calculus. In particular, in order to compare our method with the formulations in the literature, we raise some questions about interpretations of the Riemann-Liouville operators when acting on certain types of functions. In order to do so, we present the main fractional operators (Riemann-Liouville) as well as the fractional integrodifferential operator, which is a unified view of both integration and differentiation under a single operator. © Sociedade Brasileira de Física.
Nesse trabalho estudamos a resolução de um caso particular da equaçãoo hipergeométrica confluente, a equação de Bessel de ordem p, utilizando a teoria do cálculo de ordem não inteira. Em particular, a fim de comparar com a literatura existente, expomos os resultados da nossa investigação sob o rigor do formalismo matemático e levantamos alguns questionamentos a respeito da interpretação dos operadores de Riemann-Liouville quando agindo em certas funções. Para tanto, introduzimos as principais formulações dos operadores fracionários (Riemann-Liouville), assim como o operador de integrodiferenciação fracionária que é a tentativa de se expressar ambos operadores de integração e diferenciação fracionárias de forma unificada
metadata.dc.description.abstractalternative: In this work we discuss the solvability of Bessel’s differential equation of order p, which is a particular case of the confluent hypergeometric equation, from the perspective of the theory of calculus of arbitrary order, also usually known as fractional calculus. In particular, in order to compare our method with the formulations in the literature, we raise some questions about interpretations of the Riemann-Liouville operators when acting on certain types of functions. In order to do so, we present the main fractional operators (Riemann-Liouville) as well as the fractional integrodifferential operator, which is a unified view of both integration and differentiation under a single operator
Subject: Cálculo fracionário
Equações diferenciais fracionárias
Bessel, Equações de
Country: Brasil
Editor: Sociedade Brasileira de Física
Citation: Revista Brasileira De Ensino De Fisica. Sociedade Brasileira De Fisica, v. 37, n. 3, p. , 2015.
Rights: aberto
Identifier DOI: 10.1590/S1806-11173731843
Address: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172015000300308&lng=pt&tlng=pt
Date Issue: 2015
Appears in Collections:IMECC - Artigos e Outros Documentos

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