Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative

Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative

A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation...

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Bibliographic Details
Main Authors: Nehad Ali Shah, Abdul Rauf, Dumitru Vieru, Kanokwan Sitthithakerngkiet, Poom Kumam
Format: Article
Language:English
Published: MDPI AG 2021-04-01
Series:Applied Sciences
Subjects:
radial diffusion–wave equation
fractional derivative
distributed-order
integral transforms
Online Access:https://www.mdpi.com/2076-3417/11/9/4142
Description
Summary:A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New analytical solutions to the distributed-order fractional diffusion–wave equation are determined using the Laplace and Dirichlet-Weber integral transforms. The influence of the fractional parameters on the radial groundwater flow is analyzed by numerical calculations and graphical illustrations are obtained with the software Mathcad.
ISSN:2076-3417

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