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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.

Keywords

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

R2 v1 2026-07-22T16:20:21.530Z