Solving Helmholtz Equation with Local Fractional Derivative Operators

被引：31
|
作者：
Baleanu, Dumitru [1 ,2 ,3 ]
Jassim, Hassan Kamil [4 ]
Al Qurashi, Maysaa [5 ]
机构：
[1] Cankaya Univ, Dept Math, TR-06530 Ankara, Turkey
[2] Inst Space Sci, Bucharest 077125, Romania
[3] Tshwane Univ Technol, Fac Sci, Dept Math & Stat, Private Bag X680, ZA-0001 Pretoria, South Africa
[4] Univ Thi Qar, Dept Math, Fac Educ Pure Sci, Nasiriyah 64001, Iraq
[5] King Saud Univ, Coll Sci, Dept Math, POB 2454, Ryad 11451, Saudi Arabia
来源：
FRACTAL AND FRACTIONAL | 2019年 / 3卷 / 03期
关键词：
coupled Helmholtz equation; local fractional variational iteration method; local fractional Laplace transform (LFLT); VARIATIONAL ITERATION METHOD;
D O I：
10.3390/fractalfract3030043
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The paper presents a new analytical method called the local fractional Laplace variational iteration method (LFLVIM), which is a combination of the local fractional Laplace transform (LFLT) and the local fractional variational iteration method (LFVIM), for solving the two-dimensional Helmholtz and coupled Helmholtz equations with local fractional derivative operators (LFDOs). The operators are taken in the local fractional sense. Two test problems are presented to demonstrate the efficiency and the accuracy of the proposed method. The approximate solutions obtained are compared with the results obtained by the local fractional Laplace decomposition method (LFLDM). The results reveal that the LFLVIM is very effective and convenient to solve linear and nonlinear PDEs.
引用
收藏
页码：1 / 12
页数：12
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