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

被引：2

作者：

Shah, Nehad Ali ^{[1
,2
]}

Rauf, Abdul ^{[3
]}

Vieru, Dumitru ^{[4
]}

Sitthithakerngkiet, Kanokwan ^{[5
]}

Kumam, Poom ^{[6
,7
]}

机构：

[1] Ton Duc Thang Univ, Informetr Res Grp, Ho Chi Minh City 700000, Vietnam

[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City 700000, Vietnam

[3] Air Univ Multan Campus, Dept Comp Sci & Math, Multan 60000, Pakistan

[4] Tech Univ Iasi, Dept Theoret Mech, Iasi 700050, Romania

[5] King Mongkuts Univ Technol North Bangkok KMUTNB, Dept Math, Fac Sci Appl, Intelligent & Nonlinear Dynam Innovat Res Ctr, Bangkok 10140, Thailand

[6] King Mongkuts Univ Technol Thonburi KMUTT, Fac Sci, Dept Math, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

[7] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

来源：

APPLIED SCIENCES-BASEL | 2021年 / 11卷 / 09期

关键词：

radial diffusion– wave equation; fractional derivative; distributed-order; integral transforms; MODEL; INFILTRATION; TRANSFORM; MEMORY; TESTS; SOILS;

D O I：

10.3390/app11094142

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

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.

引用

页数：13

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