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

Soft Computing - Tập 22 - Trang 773-782 - 2016
Khaled Moaddy1, Asad Freihat2, Mohammed Al-Smadi2, Eman Abuteen3, Ishak Hashim4
1Department of Mathematics, Faculty of Science and Arts, Shaqra University, Shaqra, Saudi Arabia
2Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun, Jordan
3Applied Science Department, Faculty of Engineering Technology, Al-Balqa Applied University, Amman, Jordan
4School of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia

Tóm tắt

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.

Tài liệu tham khảo

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