Relaxation Equations: Fractional Models
| Autor: | Rosa, Ester C. F. A., de Oliveira, E. Capelas |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | The relaxation functions introduced empirically by Debye, Cole-Cole, Cole-Davidson and Havriliak-Negami are, each of them, solutions to their respective kinetic equations. In this work, we propose a generalization of such equations by introducing a fractional differential operator written in terms of the Riemann-Liouville fractional derivative of order $\gamma$, $0 < \gamma \leq 1$. In order to solve the generalized equations, the Laplace transform methodology is introduced and the corresponding solutions are then presented, in terms of Mittag-Leffler functions. In the case in which the derivative's order is $\gamma=1$, the traditional relaxation functions are recovered. Finally, we presente some 2D graphs of these function. Comment: 14 pages, 8 figures |
| Databáze: | arXiv |
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