Investigation of the cumulative diminution process using the Fibonacci method and fractional calculus
Küçük Resim Yok
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier Science Bv
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this study, we investigate the cumulative diminution phenomenon for a physical quantity and a diminution process with a constant acquisition quantity in each step in a viscous medium. We analyze the existence of a dynamical mechanism that underlies the success of fractional calculus compared with standard mathematics for describing stochastic processes by proposing a Fibonacci approach, where we assume that the complex processes evolves cumulatively in fractal space and discrete time. Thus, when the differential-integral order a is attained, this indicates the involvement of the viscosity of the medium in the evolving process. The future value of the diminishing physical quantity is obtained in terms of the Mittag-Leffler function (MLF) and two rheological laws are inferred from the asymptotic limits. Thus, we conclude that the differential-integral calculus of fractional mathematics implicitly embodies the cumulative diminution mechanism that occurs in a viscous medium. (C) 2015 Elsevier B.V. All rights reserved.
Açıklama
Anahtar Kelimeler
Fibonacci numbers, Fractional calculus, Mittag-Leffler function, Rate equation
Kaynak
Physica A-Statistical Mechanics and Its Applications
WoS Q Değeri
Q1
Scopus Q Değeri
N/A
Cilt
444
