A fractional model of the diffusion equation and its analytical solution using Laplace transform

被引：52

作者：

Kumar, S. ^{[1
]}

Yildirim, A. ^{[2
]}

Khan, Yasir ^{[3
]}

Wei, L. ^{[4
]}

机构：

[1] Natl Inst Technol, Dept Math, Jamshedpur 831013, Jharkhand, India

[2] Ege Univ, Fac Sci, Dept Appl Math, TR-35100 Izmir, Turkey

[3] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[4] Xi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R China

来源：

SCIENTIA IRANICA | 2012年 / 19卷 / 04期

关键词：

Homotopy perturbation method; Laplace transform method; Fractional derivatives; Diffusion equation; Mittag-Leffler function; Analytical solution; HOMOTOPY PERTURBATION METHOD; DECOMPOSITION METHOD; COUPLING METHOD;

D O I：

10.1016/j.scient.2012.06.016

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this study, the homotopy perturbation transform method (HPTM) is performed to give analytical solutions of the time fractional diffusion equation. The HPTM is a combined form of the Laplace transform and homotopy perturbation methods. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation. A solution has been plotted for different values of alpha., and some numerical illustrations are given. (C) 2012 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.

引用

页码：1117 / 1123

页数：7

共 50 条

[1] A Fractional Model of Gas Dynamics Equations and its Analytical Approximate Solution Using Laplace Transform
Kumar, Sunil
Kocak, Huseyin
Yildirim, Ahmet
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2012, 67 (6-7): : 389 - 396
[2] Analytical Solution of Fractional Order Diffusion Equations Using Iterative Laplace Transform Method
Feng, Yihu
Huang, Jing
PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2024, 56 (3-4): : 78 - 89
[3] ANALYTICAL SOLUTION OF THE TIME-FRACTIONAL FISHER EQUATION BY USING ITERATIVE LAPLACE TRANSFORM METHOD
Bairwa, Rajendra Kumar
JOURNAL OF RAJASTHAN ACADEMY OF PHYSICAL SCIENCES, 2018, 17 (3-4): : 191 - 200
[4] Time fractional telegraph equation and its solution by Laplace transform method
Biswas, Swapan
Das, Shantanu
Ghosh, Uttam
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2022, 15 (07)
[5] Numerical solution of the advection-diffusion equation using Laplace transform finite analytical method
Ahsan, Mahmud
INTERNATIONAL JOURNAL OF RIVER BASIN MANAGEMENT, 2012, 10 (02) : 177 - 188
[6] Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation
Sene, Ndolane
Fall, Aliou Niang
FRACTAL AND FRACTIONAL, 2019, 3 (02) : 1 - 15
[7] Analytical Solution of Physical Problems Using Local Fractional Laplace Transform
Sharma, Neetu
Mittal, Ekta
Agarwal, Surendra Kumar
NEW MATHEMATICS AND NATURAL COMPUTATION, 2024,
[8] A LAPLACE TRANSFORM TECHNIQUE FOR THE ANALYTICAL SOLUTION OF A DIFFUSION - CONVECTION EQUATION OVER A FINITE DOMAIN
DAVIS, GB
APPLIED MATHEMATICAL MODELLING, 1985, 9 (01) : 69 - 71
[9] AN ANALYTICAL SOLUTION OF THE ALGEBRAIC RICCATI EQUATION BY THE LAPLACE TRANSFORM METHOD
ARBENZ, K
AEU-ARCHIV FUR ELEKTRONIK UND UBERTRAGUNGSTECHNIK-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS, 1982, 36 (01): : 46 - 48
[10] Analytical solution of the time fractional diffusion equation and fractional convection-diffusion equation
Morales-Delgado, V. F.
Gomez-Aguilar, J. F.
Taneco-Hernandez, M. A.
REVISTA MEXICANA DE FISICA, 2019, 65 (01) : 82 - 88

← 1 2 3 4 5 →