An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like
- Departamento de Matematica Aplicada, Facultad de Informatica, Universidad Complutense de Madrid, Madrid E-28040 (Spain)
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.
- OSTI ID:
- 20699625
- Journal Information:
- Journal of Mathematical Physics, Vol. 46, Issue 11; Other Information: DOI: 10.1063/1.2121167; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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