Solution of fractional linear and bilinear time invariant system via formal power series methods
The area of fractional calculus is more than three centuries old but applications have only appeared in the past few decades. Differential equations of non-integer order are known to represent certain physical processes in a more precise way than using the usual differential equations with integer...
| Autor Principal: | Winter Arboleda, Irina Michelle |
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| Formato: | Tesis de Maestría |
| Idioma: | Inglés |
| Publicado: |
Pontificia Universidad Católica del Perú
2018
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| Materias: | |
| Acceso en línea: |
http://tesis.pucp.edu.pe/repositorio/handle/123456789/10179 |
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| Sumario: |
The area of fractional calculus is more than three centuries old but applications have only appeared in the past few decades. Differential equations of non-integer order are known to represent certain physical processes in a more precise way than using the usual differential
equations with integer order. Therefore, considering fractional calculus in the context of input-
output systems can be beneficial. A useful representation of an input-output map in control
theory is the Chen-Fliess functional series or Fliess operator. It can be viewed as a generalization of a Taylor series, and its algebraic nature is especially well suited for several
important applications. In this thesis, a general solution for a fractional linear and bilinear time invariant system via formal power series methods and Fliess operators is presented. A mathematical model (that includes a differential equation) for an input-output linear and bilinear time invariant system is very well known, both the explicit solution and the one using formal power series. However, the question of how this system behaves when a fractional
differential equation (where the derivative is of a non-integer order) has not been yet studied
from the power series point of view. This thesis focuses on two specific kind of derivatives, one
using Riemann-Liouville fractional derivatives and the other using Caputo fractional
derivatives. |
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