Soft Computing

, Volume 22, Issue 3, pp 773–782 | Cite as

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

  • Khaled MoaddyEmail author
  • Asad Freihat
  • Mohammed Al-Smadi
  • Eman Abuteen
  • Ishak Hashim
Methodologies and Application


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 \(\alpha \) 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.


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


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Khaled Moaddy
    • 1
    Email author
  • Asad Freihat
    • 2
  • Mohammed Al-Smadi
    • 2
  • Eman Abuteen
    • 3
  • Ishak Hashim
    • 4
  1. 1.Department of Mathematics, Faculty of Science and ArtsShaqra UniversityShaqraSaudi Arabia
  2. 2.Department of Applied Science, Ajloun CollegeAl-Balqa Applied UniversityAjlounJordan
  3. 3.Applied Science Department, Faculty of Engineering TechnologyAl-Balqa Applied UniversityAmmanJordan
  4. 4.School of Mathematical Sciences, Universiti Kebangsaan MalaysiaBangi, SelangorMalaysia

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