Fractional Order Calculus: Basic Concepts and Engineering Applications

Fractional Order Calculus: Basic Concepts and Engineering Applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory...

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Main Authors: Ricardo Enrique Gutiérrez, João Maurício Rosário, José Tenreiro Machado
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2010/375858
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spelling doaj-4c87af28c49546ac9ba01c9a922e87762020-11-25T00:02:52ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472010-01-01201010.1155/2010/375858375858Fractional Order Calculus: Basic Concepts and Engineering ApplicationsRicardo Enrique Gutiérrez0João Maurício Rosário1José Tenreiro Machado2Department of Mechanical Engineering, UNICAMP, 13083-970 Campinas, BrazilDepartment of Mechanical Engineering, UNICAMP, 13083-970 Campinas, BrazilDepartment of Electrical Engineering, ISEP, 4200-072 Oporto, PortugalThe fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.http://dx.doi.org/10.1155/2010/375858
collection DOAJ
language English
format Article
sources DOAJ
author Ricardo Enrique Gutiérrez
João Maurício Rosário
José Tenreiro Machado
spellingShingle Ricardo Enrique Gutiérrez
João Maurício Rosário
José Tenreiro Machado
Fractional Order Calculus: Basic Concepts and Engineering Applications
Mathematical Problems in Engineering
author_facet Ricardo Enrique Gutiérrez
João Maurício Rosário
José Tenreiro Machado
author_sort Ricardo Enrique Gutiérrez
title Fractional Order Calculus: Basic Concepts and Engineering Applications
title_short Fractional Order Calculus: Basic Concepts and Engineering Applications
title_full Fractional Order Calculus: Basic Concepts and Engineering Applications
title_fullStr Fractional Order Calculus: Basic Concepts and Engineering Applications
title_full_unstemmed Fractional Order Calculus: Basic Concepts and Engineering Applications
title_sort fractional order calculus: basic concepts and engineering applications
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2010-01-01
description The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.
url http://dx.doi.org/10.1155/2010/375858
work_keys_str_mv AT ricardoenriquegutierrez fractionalordercalculusbasicconceptsandengineeringapplications
AT joaomauriciorosario fractionalordercalculusbasicconceptsandengineeringapplications
AT josetenreiromachado fractionalordercalculusbasicconceptsandengineeringapplications
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