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

Xin Liang; Yu-Gui Yang; Feng Gao; Xiao-Jun Yang; Yi Xue

doi:10.3390/e20010078

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

Entropy (Basel). 2018 Jan 22;20(1):78. doi: 10.3390/e20010078.

Authors

Xin Liang^{1

2}, Yu-Gui Yang^{1

2}, Feng Gao^{1

2}, Xiao-Jun Yang^{1

2

3}, Yi Xue⁴

Affiliations

¹ State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China.
² School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.
³ College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.
⁴ Institute of Geotechnical Engineering, Xi'an University of Technology, Xi'an 710048, China.

Abstract

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.

Keywords: Laplace transform; anomalous advection-dispersion model; general Liouville–Caputo fractional-order derivative; series solution.

Abstract

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