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

[11] FRACTIONAL DIFFUSION EQUATION WITH DISTRIBUTED-ORDER CAPUTO DERIVATIVE
Kubica, Adam
Ryszewska, Katarzyna
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2019, 31 (02) : 195 - 243
[12] USE OF ATANGANA-BALEANU FRACTIONAL DERIVATIVE IN HELICAL FLOW OF A CIRCULAR PIPE
Abro, Kashif Ali
Khan, Ilyas
Nisar, Kottakkaran Sooppy
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (08)
[13] Analytical solutions of the 222Rn radon diffusion-advection equation through soil using Atangana-Baleanu time fractional derivative
Likene, A. A. Atangana
Nkoulou II, J. E. Ndjana
Bobbo, M. Oumar
Saidou
INDIAN JOURNAL OF PHYSICS, 2024,
[14] Numerical approximation of fractional burgers equation with Atangana-Baleanu derivative in Caputo sense
Yadav, Swati
Pandey, Rajesh K.
CHAOS SOLITONS & FRACTALS, 2020, 133
[15] Study of fractional order rabies transmission model via Atangana-Baleanu derivative
Zainab, Marya
Boulaaras, Salah
Aslam, Adnan
Shafiq, Sidra
Hussain, Takasar
Ozair, Muhammad
SCIENTIFIC REPORTS, 2024, 14 (01):
[16] ANALYTICAL TREATMENTS TO SYSTEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH MODIFIED ATANGANA-BALEANU DERIVATIVE
Al-Refai, Mohammed
Syam, Muhammed I.
Baleanu, Dumitru
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2023, 31 (10)
[17] Fuzzy fractional delay integro-differential equation with the generalized Atangana-Baleanu fractional derivative
Wang, Guotao
Feng, Meihua
Zhao, Xianghong
Yuan, Hualei
DEMONSTRATIO MATHEMATICA, 2024, 57 (01)
[18] Chaotic analysis of Atangana-Baleanu derivative fractional order Willis aneurysm system
Gao, Fei
Li, Wen-Qin
Tong, Heng-Qing
Li, Xi-Ling
CHINESE PHYSICS B, 2019, 28 (09)
[19] KORTEWEG-DE VRIES-BURGERS (KDVB) EQUATION WITH ATANGANA-BALEANU DERIVATIVE WITH FRACTIONAL ORDER
Dokuyucu, M. A.
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2020, 10 (03): : 727 - 733
[20] Study of Fuzzy Fractional Third-Order Dispersive KdV Equation in a Plasma under Atangana-Baleanu Derivative
Areshi, Mounirah
El-Tantawy, S. A.
Alotaibi, B. M.
Zaland, Shamsullah
JOURNAL OF FUNCTION SPACES, 2022, 2022

← 1 2 3 4 5 →