Stationarity-conservation laws for certain linear fractional differential equations
Mathematical Physics
2009-11-07 v1 math.MP
Abstract
The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.
Cite
@article{arxiv.math-ph/0104025,
title = {Stationarity-conservation laws for certain linear fractional differential equations},
author = {M. Klimek},
journal= {arXiv preprint arXiv:math-ph/0104025},
year = {2009}
}
Comments
28 pages