Stationarity-conservation laws for certain linear fractional differential equations

The Leibniz rule for the fractional Riemann-Liouville derivative is studied in the algebra of functions defined by Laplace convolution. This algebra a nd the derived Leibniz rule is used in construction of an explicit form of stationary-conserved currents for linear fractional differential equations. The examples of fractional diffusion in 1 + 1 and fractional diffusion in d + 1 dimensions are discussed in detail, The results are generalized to th e mixed fractional-differential and mixed sequential fractional-differentia l systems for which the stationarity-conservation laws are obtained. The de rived currents are used in construction of stationary nonlocal charges.