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In this paper, an anomalous advection-dispersion model involving a new general Liouville-Caputo fractional-order derivative is addressed for the first time. The series solutions of the general fractional advection-dispersion equations are obtained with the aid of the Laplace transform. The results are given to demonstrate the efficiency of the proposed formulations to describe the anomalous advection dispersion processes.

Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions