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

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[1] Homotopy perturbation method for nonlinear partial differential equations of fractional order [J].

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PHYSICS LETTERS A, 2007, 365 (5-6) :345-350

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