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

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