Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions
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 a...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-01-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/20/1/78 |
| _version_ | 1818035582482251776 |
|---|---|
| author | Xin Liang Yu-Gui Yang Feng Gao Xiao-Jun Yang Yi Xue |
| author_facet | Xin Liang Yu-Gui Yang Feng Gao Xiao-Jun Yang Yi Xue |
| author_sort | Xin Liang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T06:57:21Z |
| format | Article |
| id | doaj.art-270cb6dc392145e0a40d7be39b9afb83 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-12-10T06:57:21Z |
| publishDate | 2018-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-270cb6dc392145e0a40d7be39b9afb832022-12-22T01:58:25ZengMDPI AGEntropy1099-43002018-01-012017810.3390/e20010078e20010078Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series SolutionsXin Liang0Yu-Gui Yang1Feng Gao2Xiao-Jun Yang3Yi Xue4State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaInstitute of Geotechnical Engineering, Xi’an University of Technology, Xi’an 710048, ChinaIn 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.http://www.mdpi.com/1099-4300/20/1/78anomalous advection-dispersion modelgeneral Liouville–Caputo fractional-order derivativeseries solutionLaplace transform |
| spellingShingle | Xin Liang Yu-Gui Yang Feng Gao Xiao-Jun Yang Yi Xue Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions Entropy anomalous advection-dispersion model general Liouville–Caputo fractional-order derivative series solution Laplace transform |
| title | Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions |
| title_full | Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions |
| title_fullStr | Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions |
| title_full_unstemmed | Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions |
| title_short | Anomalous Advection-Dispersion Equations within General Fractional-Order Derivatives: Models and Series Solutions |
| title_sort | anomalous advection dispersion equations within general fractional order derivatives models and series solutions |
| topic | anomalous advection-dispersion model general Liouville–Caputo fractional-order derivative series solution Laplace transform |
| url | http://www.mdpi.com/1099-4300/20/1/78 |
| work_keys_str_mv | AT xinliang anomalousadvectiondispersionequationswithingeneralfractionalorderderivativesmodelsandseriessolutions AT yuguiyang anomalousadvectiondispersionequationswithingeneralfractionalorderderivativesmodelsandseriessolutions AT fenggao anomalousadvectiondispersionequationswithingeneralfractionalorderderivativesmodelsandseriessolutions AT xiaojunyang anomalousadvectiondispersionequationswithingeneralfractionalorderderivativesmodelsandseriessolutions AT yixue anomalousadvectiondispersionequationswithingeneralfractionalorderderivativesmodelsandseriessolutions |