Stationarity-conservation laws for fractional differential equations with variable coefficients

In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1 + 1)- and (d + 1)-dimensional space and the fractional Klein-Kramers equation.