Maria Pilar Velasco
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Maria Pilar Velasco has a total of 38 co-authors. Here are the top co-authors by number of shared publications:
- Juan J. Trujillo
Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, Tenerife, Spain
10 shared publications - Luis Vázquez
Universidad Complutense de Madrid
10 shared publications - Salvador Jiménez
Universidad Politécnica de Madrid
7 shared publications - Carlos Lizama
Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencia, Universidad de Santiago de Chile, Santiago, Chile
6 shared publications - David Usero
Universidad Complutense de Madrid
6 shared publications - Jose Luis Vazquez-Poletti
Universidad Complutense de Madrid
6 shared publications
Latest Publications
- Open Access
- 20 March 2024
- Published by Springer Nature in Fractional Calculus and Applied Analysis
- Vol. 27 (3) , 1017-1047
Rich phenomenology of the solutions in a fractional Duffing equation
In this paper, we characterize the chaos in the Duffing equation with negative linear stiffness and a fractional damping term given by a Caputo fractional derivative of order $$\alpha $$ ranging from 0 to 2. We use two different numerical methods to compute the solutions, one of them new. We discriminate between regular and chaotic solutions by means of the attractor in the phase space and the values of the Lyapunov Characteristic Exponents. For this, we have extended a linear approximation method to this equation. The system is very rich with distinct behaviours. In the limits $$\alpha $$ to 0 or $$\alpha $$ to 2, the system tends to basically the same undamped system with a behaviour clearly different from the classical Duffing equation.- 20 March 2024
- Published by Springer Nature in Fractional Calculus and Applied Analysis
- Vol. 27 (3) , 1017-1047
Open AccessRich phenomenology of the solutions in a fractional Duffing equation
In this paper, we characterize the chaos in the Duffing equation with negative linear stiffness and a fractional damping term given by a Caputo fractional derivative of order $$\alpha $$ ranging from 0 to 2. We use two different numerical methods to compute the solutions, one of them new. We discriminate between regular and chaotic solutions by means of the attractor in the phase space and the values of the Lyapunov Characteristic Exponents. For this, we have extended a linear approximation method to this equation. The system is very rich with distinct behaviours. In the limits $$\alpha $$ to 0 or $$\alpha $$ to 2, the system tends to basically the same undamped system with a behaviour clearly different from the classical Duffing equation. - 11 May 2022
- Published by Springer Nature
- p. 45-54
About the Simulations of Maxwell Equations: Some Applications
- 11 May 2022
- Published by Springer Nature
- p. 45-54
About the Simulations of Maxwell Equations: Some Applications
- 1 April 2022
- Published by ASME International in Journal of Computational and Nonlinear Dynamics
- Vol. 17 (8)
From Eikonal to Antieikonal Approximations: Competition of Scales in the Framework of Schrödinger and Classical Wave Equation
We present a description of certain limits associated with the Schrödinger equation, the classical wave equation, and Maxwell equations. Such limits are mainly characterized by the competition of two fundamental scales. More precisely: (1) The competition of an exploratory wavelength and the scale of fluctuations is associated with the media where the propagation takes place. From that, the universal behaviors arise eikonal and anti-eikonal. (2) In the context above, it is specially relevant and promising the study of propagation of electromagnetic waves in a media with a self-similar structure, like a fractal one. These systems offer the suggestive scenario where the eikonal and anti-eikonal behaviors are simultaneous. This kind of study requires large and massive computations that are mainly possible in the framework of the cloud computing. Recently, we started to carry out this task. (3) Finally and as a collateral aspect, we analyze the Planck constant in the interval .- 1 April 2022
- Published by ASME International in Journal of Computational and Nonlinear Dynamics
- Vol. 17 (8)
From Eikonal to Antieikonal Approximations: Competition of Scales in the Framework of Schrödinger and Classical Wave Equation
We present a description of certain limits associated with the Schrödinger equation, the classical wave equation, and Maxwell equations. Such limits are mainly characterized by the competition of two fundamental scales. More precisely: (1) The competition of an exploratory wavelength and the scale of fluctuations is associated with the media where the propagation takes place. From that, the universal behaviors arise eikonal and anti-eikonal. (2) In the context above, it is specially relevant and promising the study of propagation of electromagnetic waves in a media with a self-similar structure, like a fractal one. These systems offer the suggestive scenario where the eikonal and anti-eikonal behaviors are simultaneous. This kind of study requires large and massive computations that are mainly possible in the framework of the cloud computing. Recently, we started to carry out this task. (3) Finally and as a collateral aspect, we analyze the Planck constant in the interval .- 10 March 2022
- Published by Springer Nature
- p. 89-104
From Radiation and Space Exploration to the Fractional Calculus
- 10 March 2022
- Published by Springer Nature
- p. 89-104
From Radiation and Space Exploration to the Fractional Calculus
- Open Access
- 2 June 2020
- Published by MDPI AG in Mathematics
- Vol. 8 (6) , 893
About Some Possible Implementations of the Fractional Calculus
We present a partial panoramic view of possible contexts and applications of the fractional calculus. In this context, we show some different applications of fractional calculus to different models in ordinary differential equation (ODE) and partial differential equation (PDE) formulations ranging from the basic equations of mechanics to diffusion and Dirac equations.
- 2 June 2020
- Published by MDPI AG in Mathematics
- Vol. 8 (6) , 893
Open AccessAbout Some Possible Implementations of the Fractional Calculus
We present a partial panoramic view of possible contexts and applications of the fractional calculus. In this context, we show some different applications of fractional calculus to different models in ordinary differential equation (ODE) and partial differential equation (PDE) formulations ranging from the basic equations of mechanics to diffusion and Dirac equations.
- 7 June 2019
- Published by Springer Nature in Communications on Applied Mathematics and Computation
- Vol. 1 (2) , 253-261
Public "Cloud" Provisioning for Venus Express VMC Image Processing
- 7 June 2019
- Published by Springer Nature in Communications on Applied Mathematics and Computation
- Vol. 1 (2) , 253-261
Public "Cloud" Provisioning for Venus Express VMC Image Processing
- Open Access
- 1 January 2019
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 39 (5) , 2679-2708
On well-posedness of vector-valued fractional differential-difference equations
We develop an operator-theoretical method for the analysis on well posedness of partial differential-difference equations that can be modeled in the form$ \begin{equation*} (*) \left\{\begin{array}{rll} \Delta^{\alpha} u(n) & = & Au(n+2) + f(n,u(n)), \quad n \in \mathbb{N}_0, \,\, 1< \alpha \leq 2; \\ u(0) & = & u_0;\\ u(1) & = & u_1, \end{array}\right. \end{equation*} $where \begin{document}$ A $\end{document} is a closed linear operator defined on a Banach space \begin{document}$ X $\end{document}. Our ideas are inspired on the Poisson distribution as a tool to sampling fractional differential operators into fractional differences. Using our abstract approach, we are able to show existence and uniqueness of solutions for the problem (*) on a distinguished class of weighted Lebesgue spaces of sequences, under mild conditions on sequences of strongly continuous families of bounded operators generated by \begin{document}$ A, $\end{document} and natural restrictions on the nonlinearity \begin{document}$ f $\end{document}. Finally we present some original examples to illustrate our results.- 1 January 2019
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 39 (5) , 2679-2708
Open AccessOn well-posedness of vector-valued fractional differential-difference equations
We develop an operator-theoretical method for the analysis on well posedness of partial differential-difference equations that can be modeled in the form$ \begin{equation*} (*) \left\{\begin{array}{rll} \Delta^{\alpha} u(n) & = & Au(n+2) + f(n,u(n)), \quad n \in \mathbb{N}_0, \,\, 1< \alpha \leq 2; \\ u(0) & = & u_0;\\ u(1) & = & u_1, \end{array}\right. \end{equation*} $where \begin{document}$ A $\end{document} is a closed linear operator defined on a Banach space \begin{document}$ X $\end{document}. Our ideas are inspired on the Poisson distribution as a tool to sampling fractional differential operators into fractional differences. Using our abstract approach, we are able to show existence and uniqueness of solutions for the problem (*) on a distinguished class of weighted Lebesgue spaces of sequences, under mild conditions on sequences of strongly continuous families of bounded operators generated by \begin{document}$ A, $\end{document} and natural restrictions on the nonlinearity \begin{document}$ f $\end{document}. Finally we present some original examples to illustrate our results. - 14 August 2018
- Published by Global Science Press in International Journal of Numerical Analysis and Modeling
- Vol. 15 (1-2) , 74-85
Modeling and Simulation of the Atmospheric Dust Dynamic: Fractional Calculus and Cloud Computing
The dust aerosols have an important effect on the solar radiation in the Martial atmosphere and both surface and atmospheric heating rates, which are also basic drivers of atmospheric dynamics. Aerosols cause an attenuation of the solar radiation traversing the atmosphere and this attenuation is modeled by the Lambert-Beer-Bouguer law, where the aerosol optical thickness plays an important role. Through Angstrom law, the aerosol optical thickness can be approximated and this law allows to model attenuation of the solar radiation traversing the atmosphere by a fractional diffusion equation. The analytical solution is available in the case of one space dimension. When we extend the fractional diffusion equation to the case of two or more space variables, we need large and massive computations to approach numerically the solutions. In this case a suitable strategy is to use the cloud computing to carry out the simulations. We present an introduction to cloud computing applied to the fractional diffusion equation in one dimension.
- 14 August 2018
- Published by Global Science Press in International Journal of Numerical Analysis and Modeling
- Vol. 15 (1-2) , 74-85
Modeling and Simulation of the Atmospheric Dust Dynamic: Fractional Calculus and Cloud Computing
The dust aerosols have an important effect on the solar radiation in the Martial atmosphere and both surface and atmospheric heating rates, which are also basic drivers of atmospheric dynamics. Aerosols cause an attenuation of the solar radiation traversing the atmosphere and this attenuation is modeled by the Lambert-Beer-Bouguer law, where the aerosol optical thickness plays an important role. Through Angstrom law, the aerosol optical thickness can be approximated and this law allows to model attenuation of the solar radiation traversing the atmosphere by a fractional diffusion equation. The analytical solution is available in the case of one space dimension. When we extend the fractional diffusion equation to the case of two or more space variables, we need large and massive computations to approach numerically the solutions. In this case a suitable strategy is to use the cloud computing to carry out the simulations. We present an introduction to cloud computing applied to the fractional diffusion equation in one dimension.
- Open Access
- 28 December 2017
- Published by MDPI AG in Fractal and Fractional
- Vol. 2 (1) , 1
Fractional Diffusion Models for the Atmosphere of Mars
The dust aerosols floating in the atmosphere of Mars cause an attenuation of the solar radiation traversing the atmosphere that cannot be modeled through the use of classical diffusion processes. However, the definition of a type of fractional diffusion equation offers a more accurate model for this dynamic and the second order moment of this equation allows one to establish a connection between the fractional equation and the Ångstrom law that models the attenuation of the solar radiation. In this work we consider both one and three dimensional wavelength-fractional diffusion equations, and we obtain the analytical solutions and numerical methods using two different approaches of the fractional derivative.
- 28 December 2017
- Published by MDPI AG in Fractal and Fractional
- Vol. 2 (1) , 1
Open AccessFractional Diffusion Models for the Atmosphere of Mars
The dust aerosols floating in the atmosphere of Mars cause an attenuation of the solar radiation traversing the atmosphere that cannot be modeled through the use of classical diffusion processes. However, the definition of a type of fractional diffusion equation offers a more accurate model for this dynamic and the second order moment of this equation allows one to establish a connection between the fractional equation and the Ångstrom law that models the attenuation of the solar radiation. In this work we consider both one and three dimensional wavelength-fractional diffusion equations, and we obtain the analytical solutions and numerical methods using two different approaches of the fractional derivative.
- 13 October 2016
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 216 (1) , 471-505
Cesàro sums and algebra homomorphisms of bounded operators
- 13 October 2016
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 216 (1) , 471-505
Cesàro sums and algebra homomorphisms of bounded operators