Percorrer por autor "Trujillo, Juan J."
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- Controllability results for impulsive mixed type functional integro-differential evolution equations with nonlocal conditionsPublication . Machado, J. A. Tenreiro; Ravichandran, Chokkalingam; Rivero, Margarita; Trujillo, Juan J.In this paper, we establish the controllability for a class of abstract impulsive mixed-type functional integro-differential equations with finite delay in a Banach space. Some sufficient conditions for controllability are obtained by using the Mönch fixed point theorem via measures of noncompactness and semigroup theory. Particularly, we do not assume the compactness of the evolution system. An example is given to illustrate the effectiveness of our results.
- Fractional calculus: a survey of useful formulasPublication . Valério, D.; Trujillo, Juan J.; Rivero, Margarita; Machado, J. A. Tenreiro; Baleanu, DumitruThis paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.
- Fractional signals and systems - editorialPublication . Ortigueira, Manuel D.; Machado, J. A.Tenreiro; Trujillo, Juan J.; Vinagre, Blas M.The word fractional acquired a new glamour at the beginning of the XXI century. Searching the web we count millions of references about this topic. In fact, we find it in a lot of apparently different scientific fields that in a first glance seem not to have any connection, but that verified to be a good strategy to adopt in their studies. Here we focus our attention into two of the most interesting and useful fractional areas: the Fractional Calculus and the Fractional Fourier transform.
- Integer/fractional decomposition of the impulse response of fractional linear systemsPublication . Ortigueira, Manuel D.; Machado, J. A. Tenreiro; Rivero, Margarita; Trujillo, Juan J.The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.
- Observability of nonlinear fractional dynamical systemsPublication . Balachandran, K.; Govindaraj, V.; Rivero, Margarita; Machado, J. A. Tenreiro; Trujillo, Juan J.We study the observability of linear and nonlinear fractional differential systems of order 0 < α < 1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.
- On development of fractional calculus during the last fifty yearsPublication . 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.
- Science metrics on fractional calculus development since 1966Publication . 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.
- Stability of fractional order systemsPublication . Rivero, Margarita; Rogosin, Sergei V.; Machado, J. A. Tenreiro; Trujillo, Juan J.The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.
- Theory and Applications of Fractional Order Systems 2016Publication . Caponetto, Riccardo; Trujillo, Juan J.; Tenreiro Machado, J. A.In the last decades noninteger differentiation became a popular tool for modeling the complex behaviours of physical systems from diverse domains such as mechanics, electricity, chemistry, biology, and economics. Numerous studies have validated the novel perspective demonstrating fractional order models that better characterize many real-world physical systems by means of differential operators of noninteger order. The long-range temporal or spatial dependence phenomena inherent to the fractional order systems (FOS) present unique and intriguing peculiarities, not supported by their integer order counterpart, which raise exciting challenges and opportunities related to the development of modelling, control, and estimation methodologies involving fractional order dynamics.