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.
Highlights
IntroductionFractional differential equations have been widely applied to describe the anomalous phenomena in multiple scientific fields, such as physical chemistry, environmental engineering, biology, etc. [1,2,3,4]
Fractional differential equations have been widely applied to describe the anomalous phenomena in multiple scientific fields, such as physical chemistry, environmental engineering, biology, etc. [1,2,3,4].In general, the fractional advection-dispersion models with the Caputo fractional derivative [5] may match the real observation better than the classical advection-dispersion models [6,7], which were applied to describe the transport of chemical pollutants in shale gas exploitation [8]
In view of the above, the principal objective of this paper is to explore the anomalous advection-dispersion equation describing the pollutant transport in shale gas exploitation within the general Liouville–Caputo fractional derivative operator of Wiman type
Summary
Fractional differential equations have been widely applied to describe the anomalous phenomena in multiple scientific fields, such as physical chemistry, environmental engineering, biology, etc. [1,2,3,4]. The new general Liouville–Caputo fractional derivative operator of Wiman type was considered to describe the anomalous relaxation behavior in [18]. Liouville–Caputo fractional derivative operator of Wiman type has not been applied to model the advection-dispersion processes. In view of the above, the principal objective of this paper is to explore the anomalous advection-dispersion equation describing the pollutant transport in shale gas exploitation within the general Liouville–Caputo fractional derivative operator of Wiman type.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
