On the Mittag-Leffler function / Sobre a função de Mittag-Leffler
AUTOR(ES)
Danilo Castro Rosendo
DATA DE PUBLICAÇÃO
2008
RESUMO
This work presents an introductory study of a second order, linear and homogeneous, ordinary differential equation with three singular regular points, including a singularity at the infinity. We obtain the hypergeometric equation and, by means of the Frobenius method, we introduce the hypergeometric function which is regular at the origin. By a convenient limit process we obtain the confluent hypergeometric equation which has the confluent hypergeometric function as a regular solution at the origin. We introduce the Mittag-Leffler function as a generalization of the exponential function and present a relation with the confluent hypergeometric function. Finally, we present the so-called fractional ordinary differential equation and as an application we discuss the fractional harmonic oscillator
ASSUNTO(S)
oscilador harmonico fracionario mittag-leffler function calculo fracionario hypergeometric functions funções de mittag-leffler fractional harmonic oscillators funções hipergeometricas fractional calculus
ACESSO AO ARTIGO
http://libdigi.unicamp.br/document/?code=000430890Documentos Relacionados
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