Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4525267 | Advances in Water Resources | 2016 | 5 Pages |
•Derivation of the two-sided fractional conservation of mass equation using Mean Value Theorems for fractional derivatives.•Explanation of the structure of the fractional derivatives appearing in the derivation of fractional conservation of mass equation when Taylor series is used.•Derivation of the right fractional Taylor series based on the Caputo derivatives.•Showing the steps in the derivation of the corresponding fractional advection-dispersion equation.
A two-sided fractional conservation of mass equation is derived by using left and right fractional Mean Value Theorems. This equation extends the one-sided fractional conservation of mass equation of Wheatcraft and Meerschaert. Also, a two-sided fractional advection-dispersion equation is derived. The derivations are based on Caputo fractional derivatives.