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

[41] New Homotopy Perturbation Method for Solving Nonlinear Differential Equations and Fisher Type Equation [J].

Fatima, Nahid .

2017 IEEE INTERNATIONAL CONFERENCE ON POWER, CONTROL, SIGNALS AND INSTRUMENTATION ENGINEERING (ICPCSI), 2017, :1669-1673

[42] Convergence of the homotopy perturbation method for partial differential equations [J].

Biazar, J. ;

Ghazvini, H. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (05) :2633-2640

[43] Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations [J].

Momani, Shaher ;

Odibat, Zaid .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (7-8) :910-919

[44] Using an enhanced homotopy perturbation method in fractional differential equations via deforming the linear part [J].

Hosseinnia, S. H. ;

Ranjbar, A. ;

Momani, S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (12) :3138-3149

[45] Convergence analysis of homotopy perturbation method for Volterra integro-differential equations of fractional order [J].

Sayevand, K. ;

Fardi, M. ;

Moradi, E. ;

Boroujeni, F. Hemati .

ALEXANDRIA ENGINEERING JOURNAL, 2013, 52 (04) :807-812

[46] Homotopy Perturbation Pade Technique for Solving Fractional Riccati Differential Equations [J].

Jafari, H. ;

Kadkhoda, N. ;

Tajadodi, H. ;

Matikolai, S. A. Hosseini .

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2010, 11 :271-275

[47] MODIFIED HOMOTOPY PERTURBATION METHOD COUPLED WITH LAPLACE TRANSFORM FOR FRACTIONAL HEAT TRANSFER AND POROUS MEDIA EQUATIONS [J].

Yan, Li-Mei .

THERMAL SCIENCE, 2013, 17 (05) :1409-1414

[48] Solving a system of nonlinear fractional partial differential equations using homotopy analysis method [J].

Jafari, H. ;

Seifi, S. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (05) :1962-1969

[49] A NEW MODIFICATION OF THE REDUCED DIFFERENTIAL TRANSFORM METHOD FOR NONLINEAR FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS [J].

Khalouta, Ali ;

Kadem, Abdelouahab .

JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS, 2020, 19 (03) :45-58

[50] Existence of solution for an infinite system of nonlinear integral equations via measure of noncompactness and homotopy perturbation method to solve it [J].

Hazarika, Bipan ;

Srivastava, H. M. ;

Arab, Reza ;

Rabbani, Mohsen .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 343 :341-352

← 1 2 3 4 5 →