Fractional mechanical oscillators
In this contribution we propose a new fractional differential equation to describe the mechanical oscillations of a simple system. In particular, we analyze the systems mass-spring and spring-damper. The order of the derivatives is 0 < y ≤ 1. In order to be consistent with the physical equation a...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | México |
| Institución: | Universidad de Guanajuato |
| Repositorio: | Redalyc-UG |
| OAI Identifier: | oai:redalyc.org:57023376011 |
| Acceso en línea: | https://www.redalyc.org/articulo.oa?id=57023376011 |
| Access Level: | acceso abierto |
| Palabra clave: | Física, Astronomía y Matemáticas caputo derivative Fractional calculus fractional structures mechanical oscillators |
| Sumario: | In this contribution we propose a new fractional differential equation to describe the mechanical oscillations of a simple system. In particular, we analyze the systems mass-spring and spring-damper. The order of the derivatives is 0 < y ≤ 1. In order to be consistent with the physical equation a new parameter ¾ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative ¿ and the new parameter ¾ is found. Due to this relation the solutions of the corresponding fractional differential equations are given in terms of the Mittag-Leffler function depending only on the parameter y. The classical cases are recovered by taking the limit when y = 1. |
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