Encontrados 11 documentos, a visualizar página 1 de 2
On development of fractional calculus during the last fifty years
Machado, J. A. Tenreiro; Galhano, Alexandra; Trujillo, Juan J.Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.
Fractional dynamics and MDS visualization of earthquake phenomena
Lopes, António M.; Machado, J. A. Tenreiro; Pinto, Carla M. A.; Galhano, AlexandraThis paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects t...
Symbolic fractional dynamics
Machado, J. A. Tenreiro; Galhano, AlexandraFractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the...
Science metrics on fractional calculus development since 1966
Machado, J. A. Tenreiro; Galhano, Alexandra; Trujillo, Juan J.During the last fifty years the area of Fractional Calculus verified a considerable progress. This paper analyzes and measures the evolution that occurred since 1966.
Fractional order inductive phenomena based on the skin effect
Machado, J. A. Tenreiro; Galhano, AlexandraThe Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genet...
Uma abordagem estatística à modelização de manipuladores robóticos
Galhano, Alexandra Maria Soares FerreiraDissertação apresentada para obtenção do grau de Doutor em Engenharia Electrotécnica e de Computadores, na Faculdade de Engenharia da Universidade do Porto, sob a orientação do Prof. Doutor J. L. Martins de Carvalho
Optimal approximation of fractional derivatives through discrete-time fractions...
Machado, J. A. Tenreiro; Galhano, Alexandra; Oliveira, Anabela; Tar, József K.This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.
Some applications of fractional calculus in engineering
Machado, J. A. Tenreiro; Silva, Manuel F.; Barbosa, Ramiro S.; Jesus, Isabel S.; Reis, Cecília; Marcos, Maria da Graça; Galhano, AlexandraFractional 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 est...
Approximating fractional derivatives through the generalized mean
Machado, J. A. Tenreiro; Galhano, Alexandra; Oliveira, Anabela; Tar, József K.This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm.
Performance of fractional PID algorithms controlling nonlinear systems with sat...
Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Galhano, AlexandraThe development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided th...
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