Stationarity-conservation laws for certain linear fractional differential equations

Details Stationarity-conservation laws for certain linear fractional differential equations Stationarity-conservation laws for certain linear fractional differential equations

2001-04-18

arxiv.org/abs/math-ph/0104025v1

Physics

Mathematical Physics

28 pages

Scientific paper

10.1088/0305-4470/34/31/311

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.

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