Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach

Khaled Moaddy, Asad Freihat, Mohammed Al-Smadi, Eman Abuteen, Ishak Hashim

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

In this paper, we present a reliable multistep numerical approach, so-called Multistep Generalized Differential Transform (MsGDT), to obtain accurate approximate form solution for Rabinovich–Fabrikant model involving Caputo fractional derivative subjected to appropriate initial conditions. The solution methodology provides efficiently convergent approximate series solutions with easily computable coefficients without employing linearization or perturbation. The behavior of approximate solution for different values of fractional-order (Formula presented.) is shown graphically. Furthermore, the stability analysis of the suggested model is discussed quantitatively. Simulation of the MsGDT technique is also presented to show its efficiency and reliability. Numerical results indicate that the method is simple, powerful mathematical tool and fully compatible with the complexity of such problems.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalSoft Computing
DOIs
Publication statusAccepted/In press - 7 Oct 2016

Fingerprint

Fractional Order
Numerical Investigation
Transform
Caputo Fractional Derivative
Series Solution
Mathematical transformations
Linearization
Stability Analysis
Approximate Solution
Initial conditions
Perturbation
Numerical Results
Methodology
Coefficient
Model
Derivatives
Simulation
Form
Graphics

Keywords

  • Differential transform method
  • Fractional Rabinovich–Fabrikant model
  • Generalized Taylor expansion
  • Multistep approach

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Geometry and Topology

Cite this

Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach. / Moaddy, Khaled; Freihat, Asad; Al-Smadi, Mohammed; Abuteen, Eman; Hashim, Ishak.

In: Soft Computing, 07.10.2016, p. 1-10.

Research output: Contribution to journalArticle

Moaddy, Khaled ; Freihat, Asad ; Al-Smadi, Mohammed ; Abuteen, Eman ; Hashim, Ishak. / Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach. In: Soft Computing. 2016 ; pp. 1-10.
@article{a8977fcc83a04e4fb43ffe7fe1184648,
title = "Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach",
abstract = "In this paper, we present a reliable multistep numerical approach, so-called Multistep Generalized Differential Transform (MsGDT), to obtain accurate approximate form solution for Rabinovich–Fabrikant model involving Caputo fractional derivative subjected to appropriate initial conditions. The solution methodology provides efficiently convergent approximate series solutions with easily computable coefficients without employing linearization or perturbation. The behavior of approximate solution for different values of fractional-order (Formula presented.) is shown graphically. Furthermore, the stability analysis of the suggested model is discussed quantitatively. Simulation of the MsGDT technique is also presented to show its efficiency and reliability. Numerical results indicate that the method is simple, powerful mathematical tool and fully compatible with the complexity of such problems.",
keywords = "Differential transform method, Fractional Rabinovich–Fabrikant model, Generalized Taylor expansion, Multistep approach",
author = "Khaled Moaddy and Asad Freihat and Mohammed Al-Smadi and Eman Abuteen and Ishak Hashim",
year = "2016",
month = "10",
day = "7",
doi = "10.1007/s00500-016-2378-5",
language = "English",
pages = "1--10",
journal = "Soft Computing",
issn = "1432-7643",
publisher = "Springer Verlag",

}

TY - JOUR

T1 - Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach

AU - Moaddy, Khaled

AU - Freihat, Asad

AU - Al-Smadi, Mohammed

AU - Abuteen, Eman

AU - Hashim, Ishak

PY - 2016/10/7

Y1 - 2016/10/7

N2 - In this paper, we present a reliable multistep numerical approach, so-called Multistep Generalized Differential Transform (MsGDT), to obtain accurate approximate form solution for Rabinovich–Fabrikant model involving Caputo fractional derivative subjected to appropriate initial conditions. The solution methodology provides efficiently convergent approximate series solutions with easily computable coefficients without employing linearization or perturbation. The behavior of approximate solution for different values of fractional-order (Formula presented.) is shown graphically. Furthermore, the stability analysis of the suggested model is discussed quantitatively. Simulation of the MsGDT technique is also presented to show its efficiency and reliability. Numerical results indicate that the method is simple, powerful mathematical tool and fully compatible with the complexity of such problems.

AB - In this paper, we present a reliable multistep numerical approach, so-called Multistep Generalized Differential Transform (MsGDT), to obtain accurate approximate form solution for Rabinovich–Fabrikant model involving Caputo fractional derivative subjected to appropriate initial conditions. The solution methodology provides efficiently convergent approximate series solutions with easily computable coefficients without employing linearization or perturbation. The behavior of approximate solution for different values of fractional-order (Formula presented.) is shown graphically. Furthermore, the stability analysis of the suggested model is discussed quantitatively. Simulation of the MsGDT technique is also presented to show its efficiency and reliability. Numerical results indicate that the method is simple, powerful mathematical tool and fully compatible with the complexity of such problems.

KW - Differential transform method

KW - Fractional Rabinovich–Fabrikant model

KW - Generalized Taylor expansion

KW - Multistep approach

UR - http://www.scopus.com/inward/record.url?scp=84990938451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990938451&partnerID=8YFLogxK

U2 - 10.1007/s00500-016-2378-5

DO - 10.1007/s00500-016-2378-5

M3 - Article

AN - SCOPUS:84990938451

SP - 1

EP - 10

JO - Soft Computing

JF - Soft Computing

SN - 1432-7643

ER -