Solution of Moving Boundary Space-Time Fractional Burger's Equation

被引：17

作者：

Abdel-Salam, E. A-B ^{[1
,2
]}

Yousif, E. A. ^{[2
,3
]}

Arko, Y. A. S. ^{[2
,4
]}

Gumma, E. A. E. ^{[2
,5
]}

机构：

[1] Assiut Univ, Fac Sci, Dept Math, New Valley Branch, El Kharja 72511, Egypt

[2] Northern Border Univ, Dept Math, Fac Sci, Ar Ar 91431, Saudi Arabia

[3] Univ Khartoum, Fac Math Sci, Dept Appl Math, Khartoum 11111, Sudan

[4] Sudan Univ Sci & Technol, Fac Sci, Dept Math, Khartoum 11115, Sudan

[5] Int Univ Africa, Fac Appl & Pure Sci, Dept Math, Khartoum 14415, Sudan

来源：

JOURNAL OF APPLIED MATHEMATICS | 2014年

关键词：

PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT ALGORITHM; NUMERICAL-SOLUTION; WAVE SOLUTIONS; CALCULUS; FLOW; KDV;

D O I：

10.1155/2014/218092

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger's equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger's equation are presented graphically and discussed.

引用

页数：8

共 60 条

[31] Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results [J].

Jumarie, G. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 51 (9-10) :1367-1376

[32] New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations [J].

Jumarie, Guy .

MATHEMATICAL AND COMPUTER MODELLING, 2006, 44 (3-4) :231-254

[33] On the fractional solution of the equation f(x+y)=f(x)f(y) and its application to fractional Laplace's transform [J].

Jumarie, Guy .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (04) :1625-1643

[34] An approach via fractional analysis to non-linearity induced by coarse-graining in space [J].

Jumarie, Guy .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (01) :535-546

[35] Laplace's transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative [J].

Jumarie, Guy .

APPLIED MATHEMATICS LETTERS, 2009, 22 (11) :1659-1664

[36] Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions [J].

Jumarie, Guy .

APPLIED MATHEMATICS LETTERS, 2009, 22 (03) :378-385

[37] Finite macro-element-based volume grid deformation for large moving boundary problems [J].

Ko, Jin Hwan ;

Park, Soo Hyung ;

Park, Hoon Cheol ;

Byun, Doyoung .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, 2010, 26 (12) :1656-1673

[38] A moving mesh finite element algorithm for singular problems in two and three space dimensions [J].

Li, R ;

Tang, T ;

Zhang, PW .

JOURNAL OF COMPUTATIONAL PHYSICS, 2002, 177 (02) :365-393

[39] Two methods to solve a fractional single phase moving boundary problem [J].

Li, Xicheng ;

Wang, Shaowei ;

Zhao, Moli .

CENTRAL EUROPEAN JOURNAL OF PHYSICS, 2013, 11 (10) :1387-1391

[40] Exact analytical solutions of moving boundary problems of one-dimensional flow in semi-infinite long porous media with threshold pressure gradient [J].

Liu, Wenchao ;

Yao, Jun ;

Wang, Yueying .

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2012, 55 (21-22) :6017-6022

← 1 2 3 4 5 6 →