Showing papers by "Juan J. Trujillo published in 2014"
TL;DR: The evolution of fractional calculus is addressed and an assertive measure of the research development is established.
Abstract: 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.
130 citations
TL;DR: Substantial conditions for the existence of solutions for a class of initial value problems with integral condition for impulsive fractional integro-differential equations are established by the application of the contraction mapping principle and the Krasnoselskii fixed point theorem.
Abstract: In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problems with integral condition for impulsive fractional integro-differential equations. The results are established by the application of the contraction mapping principle and the Krasnoselskii fixed point theorem. An example is provided to illustrate the results.
48 citations
TL;DR: This paper establishes a set of sufficient conditions for the controllability of fractional semilinear integro-differential inclusions in Banach spaces via resolvent operators and uses Bohnenblust-Karlin's fixed point theorem to prove the main results.
40 citations
TL;DR: The existence and the stability of solutions for Riemann-Liouville Volterra-Stieltjes quadratic integral equations of fractional order are studied by using some fixed point theorems.
21 citations
TL;DR: In this paper, the controllability and observability properties of fractional dynamical systems in a finite dimensional space are shown to be dual, using the Mittag-Leffler matrix function.
Abstract: In this paper, we establish that the controllability and observability properties of fractional dynamical systems in a finite dimensional space are dual. Using this duality result and the Mittag-Leffler matrix function, we propose the stabilizability of fractional MIMO (Multiple-input Multipleoutput) systems. Some numerical examples are provided to show the effectiveness of the obtained results.
16 citations
TL;DR: In this paper, the authors proposed a method to solve the problem of mathematical analysis in the context of electrical engineering, where the authors used the ISEP-Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering and Mathematical Analysis.
Abstract: 1Department of Electrical, Electronics and Computer Engineering, University of Catania, Viale A. Doria 6, 95125 Catania, Italy 2ISEP-Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Antonio Bernardino de Almeida 431, 4200-072 Porto, Portugal 3Department of Mathematical Analysis, University of La Laguna, C/Astr. Francisco Sanchez s/n, La Laguna, 38271 Tenerife, Spain
10 citations
TL;DR: A fractional order hyperchaotic representation of said system is proposed using a natural fractionalization, and two different linear control methodologies to deal with the complexity which introduce such systems are proposed.
Abstract: Fractional order dynamics and chaotics systems have been recently combined, yielding interesting behaviours. In this paper, a novel integer order hyperchaotic system is considered. Then, a fractional order hyperchaotic representation of said system is proposed using a natural fractionalization. Two different linear control methodologies to deal with the complexity which introduce such systems are proposed. Those methods are able to modify the hyperchaotic behaviour of the system and force it to move towards a fixed point; i.e. steady state. These approaches give a general framework for taming such complex systems using simple linear controllers. The main tools for analysing the controlled system are Matignon stability criterion and RouthHurwitz test. Using a reliable numerical simulation, the designed system is simulated to verify the theoretical analysis.
3 citations
TL;DR: In this article, the existence of mild and classical solutions for a class of impulsive integrodifferential equations with nonlocal conditions in Banach spaces is proved. But the main results are obtained by using measure of noncompactness and semigroup theory.
Abstract: We study the existence of mild and classical solutions are proved for a class of impulsive integrodifferential equations with nonlocal conditions in Banach spaces. The main results are obtained by using measure of noncompactness and semigroup theory. An example is presented.
1 citations
01 Jan 2014
TL;DR: In this paper, the controllability and observability properties of fractional dynamical systems in a finite dimensional space are shown to be dual using the Mittag-Leffler matrix function.
Abstract: In this paper, we establish that the controllability and observability properties of fractional dynamical systems in a finite dimensional space are dual Using this duality result and the Mittag-Leffler matrix function, we propose the stabilizability of fractional MIMO (Multiple-input Multipleoutput) systems Some numerical examples are provided to show the effectiveness of the obtained results