Fractional calculus and applications / Calculo fracionario e aplicações
AUTOR(ES)
Rubens de Figueiredo Camargo
DATA DE PUBLICAÇÃO
2009
RESUMO
At this work we present a systematic and detailed study about integrals and derivatives of arbitrary order, the so-called non-integer order calculus, popularized with the name Fractional Calculus. Particularly, we discuss and solve non-integer order differential and integrodifferential equations and its applications into several areas of the knowledge, as well as introduce some new results, i.e., addition theorems, involving the Mittag-Leffler functions. After approaching the different definitions to the non-integer order derivative, we justify the fact that we use, in our applications, the definition proposed by Caputo to the fractional derivative, which is more restrictive, instead of the Riemann-Liouville ones, although this one is best known. Into the applications we presented a fractional generalization to the equation associated with the telegraph s problem, whose solution, obtained by two different ways, was the origin of two new addition theorems to the Mittag-Leffler functions. As a second application, we present the fractional version of the Lotka-Volterra system; finally, we introduce and solve the fractional generalized Langevin equation
ASSUNTO(S)
calculo fracionario mittag-leffler functions fractional calculus transformadas integrais integral transform funções de mittag-leffler equações diferenciais fracionarias fractional differential equations
ACESSO AO ARTIGO
http://libdigi.unicamp.br/document/?code=000439359Documentos Relacionados
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