On the solutions of fractional Swift Hohenberg equation with dispersion

被引：22

作者：

Vishal, K. ^{[1
]}

Das, S. ^{[1
,2
]}

Ong, S. H. ^{[2
]}

Ghosh, P. ^{[3
]}

机构：

[1] Indian Inst Technol BHU, Dept Appl Math, Varanasi 221005, Uttar Pradesh, India

[2] Univ Malaya, Inst Math Sci, Kuala Lumpur 50603, Malaysia

[3] Indian Inst Technol BHU, Dept Mech Engn, Varanasi 221005, Uttar Pradesh, India

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 11期

关键词：

Swift-Hohenberg equation; Caputo derivative; Dispersive term; Nonlinear parabolic equation; Homotopy perturbation transform method; Homotopy analysis method; Residual error; Hydrodynamic fluctuation; VARIATIONAL ITERATION METHOD; HOMOTOPY ANALYSIS METHOD;

D O I：

10.1016/j.amc.2012.12.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, the approximate solutions of the non-linear Swift Hohenberg equation with fractional time derivative in the presence of dispersive term have been obtained. The fractional derivative is described in Caputo sense. Time fractional nonlinear partial differential equations in the presence of dispersion and bifurcation parameters have been computed numerically to predict hydrodynamic fluctuations at convective instability for different particular cases and results are depicted through graphs. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：5792 / 5801

页数：10

共 29 条

[1] Adomian G., 1994, Fundamental Theories of Physics
[2] Analytical and numerical results for the Swift-Hohenberg equation
Akyildiz, F. Talay
Siginer, Dennis A.
Vajravelu, K.
Van Gorder, Robert A.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (01) : 221 - 226
[3] [Anonymous], 2011, J KING SAUD UNIV SCI, DOI DOI 10.1016/j.jksus.2010.06.024
[4] [Anonymous], 1999, FRACTIONAL DIFFERENT
[5] State space solution of implicit fractional continuous time systems
Bouagada, Djillali
Van Dooren, Paul
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2012, 15 (03) : 356 - 361
[6] Swift-Hohenberg equation with broken reflection symmetry
Burke, J.
Houghton, S. M.
Knobloch, E.
[J]. PHYSICAL REVIEW E, 2009, 80 (03):
[7] PATTERN-FORMATION OUTSIDE OF EQUILIBRIUM
CROSS, MC
HOHENBERG, PC
[J]. REVIEWS OF MODERN PHYSICS, 1993, 65 (03) : 851 - 1112
[8] Jacobian elliptic function method for nonlinear differential-difference equations
Dai, CQ
Zhang, JF
[J]. CHAOS SOLITONS & FRACTALS, 2006, 27 (04) : 1042 - 1047
[9] An approximate analytical solution of time-fractional telegraph equation
Das, S.
Vishal, K.
Gupta, P. K.
Yildirim, A.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (18) : 7405 - 7411
[10] Extended tanh-function method and its applications to nonlinear equations
Fan, EG
[J]. PHYSICS LETTERS A, 2000, 277 (4-5) : 212 - 218

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