INVESTIGATION OF FRACTIONAL ORDER SINE-GORDON EQUATION USING LAPLACE ADOMIAN DECOMPOSITION METHOD

被引：27

作者：

Ali, Amir ^{[1
]}

Gul, Zamin ^{[2
]}

Khan, Wajahat Ali ^{[1
]}

Ahmad, Saeed ^{[1
]}

Zeb, Salman ^{[1
]}

机构：

[1] Univ Malakand Dir L, Dept Math, Chakdara, Pakistan

[2] Higher Educ Dept, Peshawar, Pakistan

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2021年 / 29卷 / 05期

关键词：

Fractional Order sG Equation; Adomian Decomposition Method; Laplace Transformations; Iterative Solutions; BOUNDARY-VALUE-PROBLEMS; OPERATIONAL MATRIX-METHOD; ELECTROACOUSTIC INTERACTIONS; DIFFERENTIAL-EQUATIONS; FERROELECTRIC-CRYSTALS; SOLITONS; SYSTEM; EXISTENCE; MODELS; STATE;

D O I：

10.1142/S0218348X21501218

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We analytically investigate a nonlinear fractional-order sine-Gordon (sG) equation. The derivatives considered herein, are taken in Caputo's sense. The Laplace transform together with the Adomian decomposition method (LADM) is applied to attain analytical approximation of the aforesaid equation. The sG equation having Caputo derivative is solved in the order of series solutions and the results are confirmed by considering two examples with appropriate initial conditions. The numerical simulations are accomplished to compare with the analytical approximations, where qualitatively better agreements are achieved.

引用

页数：10

共 63 条

[1] Information transport by sine-Gordon solitons in microtubules [J].

Abdalla, E ;

Maroufi, B ;

Melgar, BC ;

Sedra, MB .

PHYSICA A, 2001, 301 (1-4) :169-173

[2]

Ahmad B, 2010, TOPOL METHOD NONL AN, V35, P295

[3] On right fractional calculus [J].

Anastassiou, George A. .

CHAOS SOLITONS & FRACTALS, 2009, 42 (01) :365-376

[4]

[Anonymous], 2015, Journal of Applied Environmental and Biological Sciences

[5]

[Anonymous], 2003, The Frenkel-Kontorova Model: Concepts, Methods, and Applications

[6]

Barone A., 1982, Physics and Applications of the Josephson Effect

[7]

Belgacem F.B.M., 2012, Math. Engg. Sci. Aeros, V3, P99

[8] Existence results for boundary value problems with non-linear fractional differential equations [J].

Benchohra, Mouffak ;

Graef, John R. ;

Hamani, Samira .

APPLICABLE ANALYSIS, 2008, 87 (07) :851-863

[9] INFLUENCE OF SOLITONS IN THE INITIAL STATE ON CHAOS IN THE DRIVEN DAMPED SINE-GORDON SYSTEM [J].

BISHOP, AR ;

FESSER, K ;

LOMDAHL, PS ;

TRULLINGER, SE .

PHYSICA D, 1983, 7 (1-3) :259-279

[10]

Bulut H., 2013, 4 INT C MATH COMP AP, P138

← 1 2 3 4 5 6 7 →