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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.
Stability of fractional order systems
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 ha...
Controllability results for impulsive mixed type functional integro-differentia...
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 give...
Observability of nonlinear fractional dynamical systems
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.
Fractional calculus: a survey of useful formulas
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.
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.
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