Publicaciones Recientes:

• Fu Jing-Li, Nie Ning-Ming, Huang Jian-Fei, S. Jiménez, Tang Yi-Fa, L. Vázquez y Zao Wei-Jia, "Noether conserved quantities and Lie point symmetries of difference Lagrange-Maxwell equations and lattices" ,  Chinesse Physics B, 18 (7), 2634-2641 (2009).

• M.P. Zorzano, L. Vázquez y S. Jiménez, "Retrieval of Ultraviolet Spectrum from Filtered Photodiode Measurements" , Submitted to Optics Letters (2008).

• G. M. Martínez, F. Valero, and L. Vázquez, "Characterization of the Convective Martian Mixed Layer" , Journal of the Atmospheric Sciences, in press.

• G. M. Martínez, F. Valero, and L. Vázquez, "Characterization of the Martian Surface Layer" , Journal of the Atmospheric Sciences 66(1), p 187-198 (2009).

• L. Rodríguez-Germá, J.J. Trujillo, L. Vázquez, M.P. Velasco, "Fractional Calculus Framework to Avoid Singularities of Differential Equations" , Fractional Calculus and Applied Analisys 11(4), (2008).

• L. Vázquez, D. Usero, "Relaciones entre los fractales y el cálculo fraccionario", Memorias de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie de Ciencias Exactas. Tomo XXXIV, "Fractales y cálculo fraccionario", 69-82, (2008).

• [pdf] J. I. Díaz, T. Pierantozzi, L. Vázquez, "On the Finite Time Extinction Phenomenon for some Nonlinear Fractional Evolution Equations" , Proceedings of Symposium on Applied Fractional Calculus (SAFC07). 2007.

• [pdf] L. Vázquez, "Fractional Equations with Internal Degrees of Freedom" , Proceedings of Symposium on Applied Fractional Calculus (SAFC07). 2007.

• [pdf] M. P. Velasco, "On Bessel Functions in the Framework of Fractional Calculus" , Proceedings of Symposium on Applied Fractional Calculus (SAFC07). 2007.

• [pdf] T. Pierantozzi, "Fractional evolution Dirac-like equations: some properties and a discrete Von Neumann's type analysis",  Jour. Comp. Appl. Math. (submitted).

• [pdf] R. Vilela-Mendes and L. Vázquez, "The Dynamical Nature of a Backlash Systema with and without Fluid Friction",  Nonlinear Dynamics, 47(4), 363-366 (2007).

• [pdf] L. Vázquez,.M.P. Zorzano and S. Jiménez, "Spectral information retrieval from integrated broadband photodiode Martian ultraviolet measurements",  Optics Letters, 32(17), 2596-2598 (2007).

• [pdf] Jingli Fu, Salvador Jiménez, Yifa Tang, and Luis Vázquez, "Construction of exact invariants of time-dependent linear nonholonomic dynamical systems", Physics Letters A (2007), doi: 10.1016/j.physleta.2007.10.027 (2007).

• [pdf] Fu Jing-Li, DaiGui-Dong, Salvador Jiménez, and Tang Yi-Fa, "Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems", Chinese Physics 16(3), 570-577 (2007).

• [pdf] C. Aguirre, D. Campos, P. Pascual and L. Vázquez, "Pattern formation and encoding rhythms analysis on a spiking/bursting neuronal network", Eur. Phys. J. Special Topics 146,169- 176 (2007).

• [pdf] D. Usero, L. Vázquez and T. Pierantozzi, "From a Fractional Mechanical Model to a Fractional Generalization of the Dirac Equation", in Proceedings of the Fifth International Conference on Engineering Computational Technology, B.H.V. Topping, G. Montero and R. Montenegro, (Editors), Civil-Comp Press, Stirlingshire, United Kingdom, paper 11, 2006.

• [pdf] T. Pierantozzi and L. Vázquez, "A Numerical Study of Fractional Evolution-Diffusion Dirac-like Equations", in Proceedings of the Fifth International Conference on Engineering Computational Technology, B.H.V. Topping, G. Montero and R. Montenegro, (Editors), Civil-Comp Press, Stirlingshire, United Kingdom, paper 20, 2006.

• [pdf] C. Aguirre, D. Campos, P. Pascual and L. Vázquez, "Computer Simulations for a Fractional Calculus Derived Internet Traffic Model", in Proceedings of the Fifth International Conference on Engineering Computational Technology, B.H.V. Topping, G. Montero and R. Montenegro, (Editors), Civil-Comp Press, Stirlingshire, United Kingdom, paper 21, 2006.

• [pdf] S. Jiménez and Y.F. Tang, "Analysis of the Numerical Methods for a Fractional Dirac Equation", in Proceedings of the Fifth International Conference on Engineering Computational Technology, B.H.V. Topping, G. Montero and R. Montenegro, (Editors), Civil-Comp Press, Stirlingshire, United Kingdom, paper 19, 2006.

• [pdf] C. Aguirre, J. Martins, R Vilela Mendes, "Dynamics and coding of a Biologically-Motivated Network" , Int. Jour. of Bif. and Chaos, 16(2), 383–394, (2006).

• [pdf] C. Aguirre, D. Campos, P. Pascual, E. Serrano, "Synchronization effects using a piecewise linear map-based spiking-bursting neuron model", Neurocomputing 69, 1116-1119, (2006).

• [pdf] Jing-Li Fu, Li-Qun Chen, Salvador Jiménez, Yi-Fa Tang, "Non-Noether symmetries and Lutzky conserved quantities for mechanico-electrical systems", Physics Letters A, 358, 5-10,(2006).

• [pdf] T. Pierantozzi, L. Vázquez, "An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like" , Jour. of Math. Phys, 46, 1135123, (2005).

• L. Vázquez, D. Usero, "Ecuaciones No locales y Modelos Fraccionarios", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, vol. 99, 203-223 (2005).

• [pdf] L. Vázquez, "Singularity Analysis of a Nonlinear Fractional Differential Equation" Rev. R. Acad. Cien. Serie A. Mat. VOL. 99 (2), 211–217 (2005).

• [pdf]L. Vázquez, "A Fruitful Interplay: From Nonlocality to Fractional Calculus" en "Nonlinear Waves, Classical and Quantum Aspects", 129-133, Ed.: V.V. Konotop y F. Abdullaev, NATO Science Series, Kluwer Academic Publishers 2004.

• L. Vázquez, "Una Panorámica del Cálculo Fraccionario y sus Aplicaciones", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 98, 17-25 (2004).

• [pdf]L. Vázquez, "Fractional Diffusion Equations with Internal Degrees of Freedom" Journal of Computational Mathematics 21, 491-494 (2003).

• [pdf] L. Vázquez y R. Vilela-Mendes, "Fractionally coupled solutions of the diffusion equation" Applied Mathematics and Computation 141, 125-130 (2003).

Histórico de Publicaciones:

Con el propósito de permitir una adecuada interpretación de las publicaciones realizadas como consecuencia de la labor investigadora realizada se han agrupado las publicaciones en varios puntos diferentes en los que tras una breve explicación se incluye la bibliografía publicada en referencia con el mismo:

• Ecuaciones de Onda No Lineales:

• S. Jiménez, P. Pascual, C. Aguirre y L. Vázquez, "A panoramic view of some perturbed nonlinear wave equations" Int. Jour. Bifurcation and Chaos, vol. 14 nº 1, pag 1-40, (2004).
• L. Vázquez, P. Pascual, S. Jiménez, "Charge Density Waves" en "Encyclopaedia of Nonlinear Science" vol. NL3299, pags. 131-132. (2004). Ed. Routledge (Londres).
• L. Vázquez, S. Jiménez, "Dispersion Relations" en "Encyclopaedia of Nonlinear Science" vol. NL3301, pags. 222-223. (2004). Ed. Routledge (Londres).
• L. Vázquez y M.P. Zorzano, "FitzHugh-Nagumo Equation" en "Encyclopaedia of Nonlinear Science" vol. NL3303, (2004). Ed. Routledge (Londres).
• L. Vázquez y M.P. Zorzano, "Virial Theorem" en "Encyclopaedia of Nonlinear Science" vol. NL3306, (2004). Ed. Routledge (Londres).
• V.V. Konotop y L. Vázquez, "Wave Propagation in Disordered Media" en "Encyclopaedia of Nonlinear Science" vol. NL3307, (2004). Ed. Routledge (Londres).



• Primeros estudios sobre efectos no locales espaciales en ecuaciones de onda:

• G. Alfimov, T. Pierantozzi y L. Vázquez, "Numerical Study of a Fractional Sine-Gordon Equation" en "Selected papers of the First IFAC (International Federation of Automatic Control) Workshop on Fractional Differentiation and its Applications", Bordeaux, France, July 19-21, 2004, Ed.: S. Samko, A. Oustaloup y J. Sabatier.
• G. Alfimov, T. Pierantozzi y L. Vázquez, "Numerical Study of a Nonlocal Sine-Gordon Equation" en "Nonlinear Waves, Classical and Quantum Aspects", 121-128, Ed.: V.V. Konotop y F. Abdullaev, NATO Science Series, Kluwer Academic Publishers 2004.
• G. Alfimov, T. Pierantozzi y L. Vázquez, "Numerical Study of a Fractional Sine-Gordon Equation" en "Fractional Differentiation And its Applications". Editores: A. Le Mahaute, J. A. Tenreiro Machado, J. C. Trigeassou y J. Sabatier. Vol.1. (2005).
• D. Usero, L. Vázquez, Journal of Physics A (enviado).



• Estudios sobre polinomios generalizados y derivadas fraccionarias:

• G. Dattoli, C. Cesarano, P.E. Ricci y L. Vázquez, "Fractional Operators, Integral Representations and Special Polynomials" International Journal of Applied Mathematics 10, 131-139 (2002).
• G. Dattoli, C. Cesarano, P.E. Ricci y L. Vázquez, "Special Polynomials and Fractional Calculus" Mathematical and Computational Modelling 37, 729-733 (2003).
• M. Meister y L. Vázquez, "Diffussion of Intrinsic Localized Modes by Attractor Hopping", Journal of Physics A: Mathematical and General 36, 11779-11790 (2003).
• G. Dattoli, P.E. Ricci, C. Cesarano y L. Vázquez., "Fractional Derivatives: Integral Representations and Generalized Polynomials" Journal of Concrete and Applicable Mathematics (2005).



• Ecuaciones diferenciales fraccionarias: Estudio de las aplicaciones y de sus soluciones:

• G. Turchetti, D. Usero, L. Vázquez "Hamiltonian Systems with Fractional Time Derivative" Tamsui Oxford Journal of Mathematical Sciences 18, 31-44 (2002).
• [pdf]L. Vázquez, "Fractional Diffusion Equations with Internal Degrees of Freedom" Journal of Computational Mathematics 21, 491-494 (2003).
• [pdf] L. Vázquez y R. Vilela-Mendes, "Fractionally coupled solutions of the diffusion equation" Applied Mathematics and Computation 141, 125-130 (2003).
• D. Usero y L. Vázquez, "Fractional Derivative: A New Formulation for Damped Systems", en "Localization and Energy Transfer in Nonlinear Systems", 296-303, Ed.: L. Vázquez, R.S. MacKay y M.P. Zorzano, World Scientific 2003.
• A.A. Kilbas, T. Pierantozzi, J.J. Trujillo y L. Vázquez, "On the Solution of Fractional Evolution Equations" Journal of Physics A: Mathematical and General 37, 3271-3283 (2004).
• L. Vázquez, "Una Panorámica del Cálculo Fraccionario y sus Aplicaciones", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 98, 17-25 (2004).
• [pdf]L. Vázquez, "A Fruitful Interplay: From Nonlocality to Fractional Calculus" en "Nonlinear Waves, Classical and Quantum Aspects", 129-133, Ed.: V.V. Konotop y F. Abdullaev, NATO Science Series, Kluwer Academic Publishers 2004.
• A.A. Kilbas, T. Pierantozzi, J.J. Trujillo y L. Vázquez, "Cauchy-type Problem for Fractional Evolution Equation" en "Selected papers of the First IFAC (International Federation of Automatic Control) Workshop on Fractional Differentiation and its Applications", Bordeaux, France, July 19-21, 2004. Ed.: S. Samko, A. Oustaloup y J. Sabatier.
• L. Vázquez, T. Pierantozzi, "No Localidad y Cálculo Fraccionario", en "Libro dedicado a la memoria del Profesor José María Fraile Peláez". (2005).
• L. Vázquez, D. Usero, "Ecuaciones No locales y Modelos Fraccionarios", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, vol. 99, 203-223 (2005).
• R. Vilela-Mendes y L. Vázquez, "The Dynamical Nature of a Backslash System with and without Fluid Friction" Nonlinear Dynamics (2006).
• T. Pierantozzi and L. Vázquez. " A Numerical Study of Fractional Evolution-Diffusion Dirac Like Equations". Proceedings of the Fifth International Conference on Engineering Computational Technology, B.H.V. Topping, G. Montero and R. Montenegro (Eds), Civil- Comp Press, Stirlingshire, Scotland, Paper 0123456789. (2006).
• D. Usero, L. Vázquez and T. Pierantozzi "From a fractional mechanical model to a fractional generalization of the Dirac equation". Proceedings of the Fifth International Conference on Engineering Computational Technology, B.H.V. Topping, G. Montero and R. Montenegro (Eds), Civil- Comp Press, Stirlingshire, Scotland. (2006).
• A.A. Kilbas, T. Pierantozzi, J.J. Trujillo y L. Vázquez, "On Generalized Fractional Evolution-Diffusion Equations" en "Fractional Differentiation And its Applications". Editores: A. Le Mahaute, J. A. Tenreiro Machado, J. C. Trigeassou y J. Sabatier. Vol.1. (2005).



• Desarrollo y verificación de esquemas numéricos convergentes y estables para ecuaciones diferenciales ordinarias, en derivadas parciales y fraccionarias, deterministas y estocásticas:

• H. Bachiri y L. Vázquez, Applied Mathematics and Computation 126, 213-229 (2002).
• S. Jiménez, I.M. Llorente, A.M. Mancho, V.M. Pérez-García y L. Vázquez, Applied Mathematics and Computation 134, 271-291 (2003).
• S. Jiménez, L. Vázquez "A dynamics approach to the Computation of Eigenvectors of Matrices" Journal of Computational Mathematics (2005, en prensa).
• S. Jiménez y Yi-Fa Tang, "Analysis of the numerical methods for a Fractional Dirac Equation" en "Proceedings of the Fifth International Conference on Engineering Computational Technology", pags. 41-42. Ed. Civil-Comp Press (2006).
• T. Pierantozzi. "Discrete Von Neumann's type analysis of Fractional Evolution Dirac like equations", J. Comp. Appl. Math. (enviado).
• D. Usero, "Fractional Taylor Series for Caputo Fractional Derivatives. Construction of Numerical Schemes", J. Comp.Appl. Math. (enviado).



• Otras publicaciones:

• L. Vázquez, "Una Panorámica de los Sistemas Complejos" en "Sistemas de Autoorganización (Instituto de Investigaciones Económicas y Sociales Francisco de Vitoria", Unión Editorial, págs. 107-123. (2004).
• L. Vázquez, "La Exploración de Marte" Revista Española de Física vol 19 nº 2, páginas: 29-35, (2005).
• Jing-Li Fu, Li-Qun Chen, S. Jiménez y Yi-Fa Tang, "Non Noether symmetries and Lutzky conserved quantities for mechanico-electrical systems", Physics Letters A, vol 358-1, pags. 5-10 (2006).
• M. P. Zorzano y L. Vázquez, "Remote Temperature retrieval from Heating or Cooling Targets", Optics Letters, Vol 31, 1420-1422, (2006).
• J. Martínez-Frías, G. Amaral y L. Vázquez, "Astrobiological Significance of Mineral son Mars Surface Environment", Reviews in Environmental Science and Biotechnology, Vol. 5, 219-231, (2006).
• Jing-Li Fu, Gui-Dong Dai, S. Jiménez y Yi-Fa Tang, "Discrete variational principle and first integral of Lagrange-Maxwell mechanico-electrical systems", Chinese Physics (enviado).

Trabajos de Investigación:

• D. Usero, "Estimación numérica de los posibles polos de una ODE", Dpto. de Matemática Aplicada, Universidad Complutense de Madrid, 2002. Director: Luis Vázquez.


• T. Pierantozzi, "Una interpolación fraccionaria entre las ecuaciones estándar de difusión y de ondas", Dpto. de Matemática Aplicada, Universidad Complutense de Madrid, 2003. Director: Luis Vázquez.

Tesis Doctorales:

• D. Usero, "Propagación de Ondas No Lineales en Medios Heterogéneos: No Localidad y Desorden" Dpto. de Matemática Aplicada, Universidad Complutense de Madrid, 2004. Director: Luis Vázquez.


• T. Pierantozzi, "Estudio de generalizaciones fraccionarias de las ecuaciones estándar de difusión y de ondas" Dpto. de Matemática Aplicada, Universidad Complutense de Madrid, 2006. Director: Luis Vázquez.