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一般分数阶导数内的反常平流-弥散方程：模型与级数解

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

作者信息

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

机构信息

State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China.

School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.

出版信息

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

DOI:10.3390/e20010078
PMID:33265165
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7512276/
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.

摘要

本文首次研究了一个涉及新型广义刘维尔-卡普托分数阶导数的反常平流-弥散模型。借助拉普拉斯变换得到了广义分数阶平流-弥散方程的级数解。给出的结果证明了所提出公式描述反常平流弥散过程的有效性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/d716fc274616/entropy-20-00078-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/956015fdd64b/entropy-20-00078-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/76a8f5553bc8/entropy-20-00078-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/dfdbc74539b8/entropy-20-00078-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/d716fc274616/entropy-20-00078-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/956015fdd64b/entropy-20-00078-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/76a8f5553bc8/entropy-20-00078-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/dfdbc74539b8/entropy-20-00078-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/742b/7512276/d716fc274616/entropy-20-00078-g004.jpg

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本文引用的文献

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Phys Rev E. 2017 Sep;96(3-1):032117. doi: 10.1103/PhysRevE.96.032117. Epub 2017 Sep 12.
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Can a Time Fractional-Derivative Model Capture Scale-Dependent Dispersion in Saturated Soils?时间分数阶导数模型能否捕捉饱和土壤中与尺度相关的弥散现象？
Ground Water. 2017 Nov;55(6):857-870. doi: 10.1111/gwat.12532. Epub 2017 Jul 10.
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A review on risk assessment techniques for hydraulic fracturing water and produced water management implemented in onshore unconventional oil and gas production.
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Sci Total Environ. 2016 Jan 1;539:478-493. doi: 10.1016/j.scitotenv.2015.09.030. Epub 2015 Sep 18.