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An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like

Pierantozzi, Teresa and Vázquez Martínez, Luis (2005) An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like. Journal of Mathematical Physics, 46 (11). ISSN 0022-2488

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Abstract

Through 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 Type:Article
Uncontrolled Keywords:Fractional differential equations, Riemann-Liouville fractional integrals and derivatives, Caputo fractional derivative, Mittag-Leffler andWright functions, Diractype equations
Subjects:Sciences > Physics > Mathematical physics
ID Code:12714
Deposited On:13 May 2011 11:13
Last Modified:06 Feb 2014 09:31

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