Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models
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- 作者：Roberto Garrappa ; roberto.garrappa@uniba.it" class="auth_mail" title="E-mail the corresponding author ; r.garrappa@gmail.com" class="auth_mail" title="E-mail the corresponding author
- 关键词：Fractional calculus ; Havriliak&ndash ; Negami model ; Grü ; nwald&ndash ; Letnikov ; Numerical methods ; Mittag-Leffler function ; Prabhakar function
- 刊名：Communications in Nonlinear Science and Numerical Simulation
- 出版年：2016
- 出版时间：September 2016
- 年：2016
- 卷：38
- 期：Complete
- 页码：178-191
- 全文大小：780 K
文摘
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Operators for the representation in the time-domain of systems with relaxation of Havriliak–Negami type are studied.
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Systems of this type are encountered in physics, mechanical engineering, electric circuits, electromagnetism, etc.
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It is provided an explicit representation in terms of fractional differences of Grunwald–Letnikov type.
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The main properties of these operators are studied.
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The discretization of the operators is also shown. The comparison with an alternative approach is numerically tested.