HOMOTOPY PERTURBATION METHOD COMBINED WITH ZZ TRANSFORM TO SOLVE SOME NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

被引：18

作者：

Riabi, Lakhdar ^{[1
]}

Belghaba, Kacem ^{[1
]}

Cherif, Mountassir Hamdi ^{[1
]}

Ziane, Djelloul ^{[1
]}

机构：

[1] Univ Oran1, Lab Math & Its Applicat LAMAP, Oran 31000, Algeria

来源：

INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS | 2019年 / 17卷 / 03期

关键词：

Caputo fractional derivative; homotopy perturbation method; ZZ transform; Fokker-Plank Equation; Schrodinger equation; KdV equation;

D O I：

10.28924/2291-8639-17-2019-406

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The idea proposed in this work is to extend the ZZ transform method to resolve the nonlinear fractional partial differential equations by combining them with the so-called homotopy perturbation method (HPM). We apply this technique to solve some nonlinear fractional equations as: nonlinear time-fractional Fokker-Planck equation, the cubic nonlinear time-fractional Schriidinger equation and the nonlinear time-fractional KdV equation. The fractional derivative is described in the Caputo sense. The results show that this is the appropriate method to solve somme models of nonlinear partial differential equations with time-fractional derivative.

引用

页码：406 / 419

页数：14

共 50 条

[21] Homotopy perturbation transform method for nonlinear equations using He's polynomials [J].

Khan, Yasir ;

Wu, Qingbiao .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (08) :1963-1967

[22] Natural homotopy perturbation method for solving nonlinear fractional gas dynamics equations [J].

Jassim, Hassan Kamil ;

Mohammed, Mayada Gassab .

INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2021, 12 (01) :812-820

[23] Comparative Study of the Nonlinear Fractional Generalized Burger-Fisher Equations Using the Homotopy Perturbation Transform Method and New Iterative Transform Method [J].

Albaidani, Mashael M. .

FRACTAL AND FRACTIONAL, 2025, 9 (06)

[24] Conformable Double Laplace Transform Method (CDLTM) and Homotopy Perturbation Method (HPM) for Solving Conformable Fractional Partial Differential Equations [J].

GadAllah, Musa Rahamh ;

Gadain, Hassan Eltayeb .

SYMMETRY-BASEL, 2024, 16 (09)

[25] Analysis of nonlinear fractional partial differential equations with the homotopy analysis method [J].

Xu, Hang ;

Liao, Shi-Jun ;

You, Xiang-Cheng .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (04) :1152-1156

[26] Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations [J].

Nawaz, Yasir .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (08) :2330-2341

[27] Extension of the Homotopy Perturbation Method for Solving Nonlinear Differential-Difference Equations [J].

Mousa, Mohamed Medhat ;

Kaltayev, Aidarkan ;

Bulut, Hasan .

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2010, 65 (12) :1060-1064

[28] A new homotopy perturbation method for system of nonlinear integro-differential equations [J].

Aminikhah, Hossein ;

Salahi, Maziar .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (05) :1186-1194

[29] RESOLVING DELAY DIFFERENTIAL EQUATIONS WITH HOMOTOPY PERTURBATION AND SUMUDU TRANSFORM [J].

Vilu, Subashini ;

Ahmad, Rokiah Rozita ;

Din, Ummul Khair Salma ;

Alias, Mohd Almie .

JURNAL TEKNOLOGI-SCIENCES & ENGINEERING, 2023, 85 (03) :145-151

[30] Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations [J].

Panda, A. ;

Santra, S. ;

Mohapatra, J. .

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2022, 68 (03) :2065-2082

← 1 2 3 4 5 →