Search results for: Juan J. Trujillo

Items from 1 to 20 out of 40 results

article

Controllability of nonlinear stochastic fractional neutral systems with multiple time varying delays in control

R. Mabel Lizzy, Krishnan Balachandran, Juan J. Trujillo

Chaos, Solitons & Fractals > 2017 > 102 > C > 162-167

Sufficient conditions for relative controllability of stochastic fractional neutral systems with bounded operator and multiple time varying delay in the control are obtained. The result is proved using an equivalent nonlinear integral equation to the system and Banach contraction principle. The controllability results are derived for systems with both Wiener and systems with Le´vy noise.

article

Exponentials and Laplace transforms on nonuniform time scales

Manuel D. Ortigueira, Delfim F.M. Torres, Juan J. Trujillo

Communications in Nonlinear Science and Numerical Simulation > 2016 > 39 > C > 252-270

We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla and delta exponentials, computed. With these exponentials, two generalised discrete-time Laplace transforms are deduced and their properties studied. These transforms...

chapter

On Deterministic Fractional Models

Margarita Rivero, Juan J. Trujillo, M. Pilar Velasco

New Trends in Nanotechnology and Fractional Calculus Applications > Mathematical tools > 123-150

This chapter is dedicated to presenting some aspects of the so-called Ordinary and/or Partial Fractional Differential Equations. During last 20 years the main underground reason that explain the interest of the applied researchers in the fractional models have been the known close link that exists between such kind of models and the so-called “Jump” stochastic models, such as the CTRW (Continuous...

article

Ulam stabilities for partial Hadamard fractional integral equations

Saïd Abbas, Wafaa Albarakati, Mouffak Benchohra, Juan J. Trujillo

Arabian Journal of Mathematics > 2016 > 5 > 1 > 1-7

This paper deals with some existence and Ulam stability results for a class of partial integral equations via Hadamard’s fractional integral, by applying Schauder’s fixed-point theorem.

article

Steady-state response of constant coefficient discrete-time differential systems

Manuel D. Ortigueira, Margarita Rivero, Juan J. Trujillo

Journal of King Saud University - Science > 2016 > 28 > 1 > 29-32

The problem of steady state output of the discrete-time fractional differential systems is studied in this paper. Based on the fact that the exponentials are the eigenfunctions of such systems, a general algorithm for the output computation when the input is the product “rising factorial.exponential” is presented. The singular case is studied and solved.

article

Relative controllability of nonlinear neutral fractional integro‐differential systems with distributed delays in control

Krishnan Balachandran, Shanmugam Divya, Luis Rodríguez‐Germá, Juan J. Trujillo

Mathematical Methods in the Applied Sciences > 39 > 2 > 214 - 224

In this paper, we establish sufficient conditions for the global relative controllability of nonlinear neutral fractional Volterra integro‐differential systems with distributed delays in control. The results are obtained by using the Mittag–Leffler functions and the Schauder fixed‐point theorem. Examples are presented to illustrate the results. Copyright © 2015 John Wiley & Sons, Ltd.

article

Existence of local solutions for differential equations with arbitrary fractional order

Mohammed M. Matar, Juan J. Trujillo

Arabian Journal of Mathematics > 2016 > 5 > 4 > 215-224

In this paper, we establish sufficient conditions for the existence of local solutions for a class of Cauchy type problems with arbitrary fractional order. The results are established by the application of the contraction mapping principle and Schaefer’s fixed point theorem. An example is provided to illustrate the applicability of the results.

article

Fractional derivatives and periodic functions

Manuel D. Ortigueira, J. Tenreiro Machado, Juan J. Trujillo

International Journal of Dynamics and Control > 2017 > 5 > 1 > 72-78

This paper studies the periodic functions in the perspective of fractional calculus application. It is shown that the fractional derivative of a periodic signal is periodic if it is defined on the whole real line. Several common fractional derivative formulations are considered, namely the Grünwald–Letnikov, Liouville and Caputo on $$\mathbb {R}$$ R , and the two-sided fractional derivatives...

article

Integer/fractional decomposition of the impulse response of fractional linear systems

Manuel D. Ortigueira, J. Tenreiro Machado, Margarita Rivero, Juan J. Trujillo

Signal Processing > 2015 > 114 > Complete > 85-88

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.

article

From a generalised Helmholtz decomposition theorem to fractional Maxwell equations

Manuel D. Ortigueira, Margarita Rivero, Juan J. Trujillo

Communications in Nonlinear Science and Numerical Simulation > 2015 > 22 > 1-3 > 1036-1049

The main objective of this paper is to propose a new generalisation of the Helmholtz decomposition theorem for both fractional time and space, which leads to four equations generalising the Maxwell equations that emerge as particular case. To get these results the well-known classical vectorial operators, gradient, divergence, curl, and laplacian are generalised to fractional orders using Grünwald–Letnikov...

article

Existence of mild solution for evolution equation with Hilfer fractional derivative

Haibo Gu, Juan J. Trujillo

Applied Mathematics and Computation > 2015 > 257 > Complete > 344-354

The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results.

article

A generalized power series and its application in the inversion of transfer functions

Manuel D. Ortigueira, Juan J. Trujillo, Valery I. Martynyuk, Fernando J.V. Coito

Signal Processing > 2015 > 107 > C > 238-245

The paper proposes a new approach to compute the impulse response of fractional order linear time invariant systems. By applying a general approach to decompose a Laplace transform into a Laurent like series, we obtain a power series that generalizes the Taylor and MacLaurin series. The algorithm is applied to the computation of the impulse response of causal linear fractional order systems. In particular...

article

Fractional signal processing and applications

Manuel D. Ortigueira, Clara M. Ionescu, J. Tenreiro Machado, Juan J. Trujillo

Signal Processing > 2015 > 107 > C > 197

article

Discrete-time differential systems

Manuel D. Ortigueira, Fernando J.V. Coito, Juan J. Trujillo

Signal Processing > 2015 > 107 > C > 198-217

In this paper we formulate a coherent discrete-time signals and systems theory taking derivative concepts as basis. Two derivatives – nabla (forward) and delta (backward) – are defined and generalized to fractional orders, obtaining two formulations that are discrete versions of the well-known Grünwald–Letnikov derivatives. The eigenfunctions of such derivatives are the so-called nabla and delta exponentials...

article

Certain fractional integral operators and the generalized multi-index Mittag-Leffler functions

Praveen Agarwal, Sergei V Rogosin, Juan J Trujillo

Proceedings - Mathematical Sciences > 2015 > 125 > 3 > 291-306

In this paper, we obtain formulas of fractional integration (of Marichev– Saigo–Maeda type) of the generalized multi-index Mittag-Leffler functions E _γ,κ[(α _j,β _j)_m; z] generalizing 2m-parametric Mittag-Leffler functions studied by Saxena and Nishimoto (J. Fract. Calc. 37 (2010] 43–52). Some interesting special cases of our main results are considered too.

article

Stabilizability of fractional dynamical systems

Krishnan Balachandran, Venkatesan Govindaraj, Luis Rodríguez-Germá, Juan J. Trujillo

Fractional Calculus and Applied Analysis > 2014 > 17 > 2 > 511-531

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.

article

On development of fractional calculus during the last fifty years

J. A. Tenreiro Machado, Alexandra M. S. F. Galhano, Juan J. Trujillo

Scientometrics > 2014 > 98 > 1 > 577-582

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.

article

An extended elastic law to represent non-linear elastic behaviour: Application in computational metal forming

Joseba Mendiguren, Juan J. Trujillo, Fernando Cortés, Lander Galdos

International Journal of Mechanical Sciences > 2013 > 77 > Complete > 57-64

This paper presents an extension of the classical elastic law. The main objective of this new law is to represent linear and non-linear behaviour for computational metal forming purposes.The extension of the model is built by means of a stress–strain relationship given by an integral equation, its kernel characterising the mentioned complex behaviour. A specific application is presented for a TRIP...

article

Fractional power-law spatial dispersion in electrodynamics

Vasily E. Tarasov, Juan J. Trujillo

Annals of Physics > 2013 > 334 > Complete > 1-23

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with...

article

Science metrics on fractional calculus development since 1966

J. Tenreiro Machado, Alexandra M. Galhano, Juan J. Trujillo

Fractional Calculus and Applied Analysis > 2013 > 16 > 2 > 479-500

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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INFONA - science communication portal

Search results for: Juan J. Trujillo

Controllability of nonlinear stochastic fractional neutral systems with multiple time varying delays in control

Exponentials and Laplace transforms on nonuniform time scales

On Deterministic Fractional Models

Ulam stabilities for partial Hadamard fractional integral equations

Steady-state response of constant coefficient discrete-time differential systems

Relative controllability of nonlinear neutral fractional integro‐differential systems with distributed delays in control

Existence of local solutions for differential equations with arbitrary fractional order

Fractional derivatives and periodic functions

Integer/fractional decomposition of the impulse response of fractional linear systems

From a generalised Helmholtz decomposition theorem to fractional Maxwell equations

Existence of mild solution for evolution equation with Hilfer fractional derivative

A generalized power series and its application in the inversion of transfer functions

Fractional signal processing and applications

Discrete-time differential systems

Certain fractional integral operators and the generalized multi-index Mittag-Leffler functions

Stabilizability of fractional dynamical systems

On development of fractional calculus during the last fifty years

An extended elastic law to represent non-linear elastic behaviour: Application in computational metal forming

Fractional power-law spatial dispersion in electrodynamics

Science metrics on fractional calculus development since 1966

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