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- Applications of fractional calculus in electrical and computer engineeringPublication . Tenreiro Machado, J. A.; Silva, Manuel; Barbosa, Ramiro; Jesus, Isabel S.; Reis, Cecília; Marcos, Maria da Graça; M. Afonso, Luís; Lima, Miguel F. M.; Pires, E. J. Solteiro; Ferreira, N. M. FonsecaFractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of several systems. This article illustrates several applications of fractional calculus in science and engineering. It has been recognized the advantageous use of this mathematical tool in the modeling and control of many dynamical systems. In this perspective, this paper investigates the use of FC in the fields of controller tuning, electrical systems, digital circuit synthesis, evolutionary computing, redundant robots, legged robots, robotic manipulators, nonlinear friction and financial modeling.
- Towards the application of fractional calculus in engineering sciencesPublication . Tenreiro Machado, J. A.; Barbosa, Ramiro; Jesus, Isabel S.; Silva, Manuel; Reis, Cecília; M. Afonso, Luís; Marcos, Maria da Graça; Lima, Miguel F. M.; Pires, Eduardo S.This article illustrates several applications of Fractional Calculus (FC) in engineering sciences. This mathematical tool will be used here to model, analyze and control various dynamical systems, such as the Van der Pol oscillator, legged robots, electrical systems, digital circuit synthesis, evolutionary computing, redundant robots and financial modelling. Their effectiveness and utility will be demonstrated.
- Fractional order dynamical systems and its applicationsPublication . Tenreiro Machado, J. A.; Barbosa, Ramiro; Jesus, Isabel S.; Silva, Manuel; Figueiredo, Lino; Reis, Cecília; Marcos, Maria da Graça; M. Afonso, Luís; Galhano, Alexandra; Duarte, Fernando B.; Lima, Miguel L.; Pires, Eduardo S.; Ferreira, Nuno M. FonsecaThis article illustrates several applications of fractional calculus (FC) in science and engineering. It has been recognized the advantageous use of this mathematical tool in the modeling and control of many dynamical systems. In this perspective, this paper investigates the use of FC in the following fields: Controller tuning; Electrical systems; Traffic systems; Digital circuit synthesis; Evolutionary computing; Redundant robots; Legged robots; Robotic manipulators; Nonlinear friction; Financial modeling.