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

共 50 条

[31] A novel approach to approximate solution of time fractional gas dynamics equation with Atangana-Baleanu derivative
Noureen, Rabia
Iqbal, Muhammad Kashif
Asgir, Maryam
Almohsen, Bandar
Azeem, Muhammad
ALEXANDRIA ENGINEERING JOURNAL, 2025, 116 : 451 - 471
[32] Controllability analysis for impulsive integro-differential equation via Atangana-Baleanu fractional derivative
Kaliraj, Kalimuthu
Thilakraj, Elumalai
Ravichandran, Chokkalingam
Sooppy Nisar, Kottakkaran
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021,
[33] Numerical approximation of Atangana-Baleanu Caputo derivative for space-time fractional diffusion equations
Wali, Mubashara
Arshad, Sadia
Eldin, Sayed M.
Siddique, Imran
AIMS MATHEMATICS, 2023, 8 (07): : 15129 - 15147
[34] Mathematical modeling of a novel fractional-order monkeypox model using the Atangana-Baleanu derivative
Biswas, A. Santanu
Aslam, B. Humaira
Tiwari, Pankaj Kumar
PHYSICS OF FLUIDS, 2023, 35 (11)
[35] Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model
Algahtani, Obaid Jefain Julaighim
CHAOS SOLITONS & FRACTALS, 2016, 89 : 552 - 559
[36] Investigation of the l-problem of Moments for Fractional-order Equations with Atangana-Baleanu Derivative
Postnov, S. S.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2022, 43 (03) : 691 - 696
[37] A FRACTIONAL SARS-COV-2 MODEL WITH ATANGANA-BALEANU DERIVATIVE: APPLICATION TO FOURTH WAVE
Chu, Yu-Ming
Yassen, Mansour F.
Ahmad, Irshad
Sunthrayuth, Pongsakorn
Khan, Muhammad Altaf
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (08)
[38] A block-centered finite difference method for the distributed-order time-fractional diffusion-wave equation
Li, Xiaoli
Rui, Hongxing
APPLIED NUMERICAL MATHEMATICS, 2018, 131 : 123 - 139
[39] Cauchy and source problems for an advection-diffusion equation with Atangana-Baleanu derivative on the real line
Avci, Derya
Yetim, Aylin
CHAOS SOLITONS & FRACTALS, 2019, 118 : 361 - 365
[40] Chelyshkov polynomials method for distributed-order time fractional nonlinear diffusion-wave equations
Heydari, M. H.
Rashid, S.
Chu, Yu-Ming
RESULTS IN PHYSICS, 2023, 47

← 1 2 3 4 5 →