A two-sided fractional conservation of mass equation

• 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.