Investigation of the cumulative diminution process using the Fibonacci method and fractional calculus
| Autor: | Z. Ok Bayrakdar, Fevzi Büyükkiliç, Doğan Demirhan |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Fibonacci number Stochastic process Mathematical analysis Function (mathematics) Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Fractional calculus symbols.namesake Discrete time and continuous time Mittag-Leffler function 0103 physical sciences symbols Applied mathematics 010306 general physics Constant (mathematics) Mathematics Physical quantity |
| Zdroj: | Physica A: Statistical Mechanics and its Applications. 444:336-344 |
| ISSN: | 0378-4371 |
| DOI: | 10.1016/j.physa.2015.09.049 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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