Person: Pierantozzi, Teresa
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First Name
Teresa
Last Name
Pierantozzi
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Area
Matemática Aplicada
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Item An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like(Journal of Mathematical Physics, 2005) Pierantozzi, Teresa; Vázquez Martínez, LuisThrough fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D’Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.Item Estudio de generalizaciones fraccionarias de las ecuaciones estándar de difusión y de ondas(2007) Pierantozzi, Teresa; Vázquez Martínez, LuisFinalmente, se ha realizado un estudio numérico de la Ecuación de Seno-Gordon Fraccionaria, que es una particular ecuación de Klein-Gordon no lineal y no local en la que la no linealidad es la función seno y la no localidad está definida por el operador de derivación fraccionario de Feller-Riesz. Esta ecuación puede considerarse como una generalización fraccionaria de un modelo de propagación de ondas no lineal, que pasa de ser no local a ser local.