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• W2265505718 abstract "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 α 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." @default.
• W2265505718 created "2016-06-24" @default.
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• W2265505718 date "2016-02-01" @default.
• W2265505718 modified "2023-10-01" @default.
• W2265505718 title "Investigation of the cumulative diminution process using the Fibonacci method and fractional calculus" @default.
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• W2265505718 doi "https://doi.org/10.1016/j.physa.2015.09.049" @default.
• W2265505718 hasPublicationYear "2016" @default.
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