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Research Papers

Comparison Between Two Reliable Methods for Accurate Solution of Fractional Modified Fornberg–Whitham Equation Arising in Water Waves

[+] Author and Article Information
A. K. Gupta

Department of Mathematics,
National Institute of Technology,
Rourkela 769008, India

S. Saha Ray

Department of Mathematics,
National Institute of Technology,
Rourkela 769008, India
e-mail: santanusaharay@yahoo.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 8, 2015; final manuscript received November 15, 2016; published online January 20, 2017. Assoc. Editor: Brian Feeny.

J. Comput. Nonlinear Dynam 12(4), 041004 (Jan 20, 2017) (10 pages) Paper No: CND-15-1329; doi: 10.1115/1.4035266 History: Received October 08, 2015; Revised November 15, 2016

In this paper, an analytical technique is proposed to determine the exact solution of fractional order modified Fornberg–Whitham equation. Since exact solution of fractional Fornberg–Whitham equation is unknown, first integral method has been applied to determine exact solutions. The solitary wave solution of fractional modified Fornberg–Whitham equation has been attained by using first integral method. The approximate solutions of fractional modified Fornberg–Whitham equation, obtained by optimal homotopy asymptotic method (OHAM), are compared with the exact solutions obtained by the first integral method. The obtained results are presented in tables to demonstrate the efficiency of these proposed methods. The proposed schemes are quite simple, effective, and expedient for obtaining solution of fractional modified Fornberg–Whitham equation.

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Figures

Grahic Jump Location
Fig. 3

Comparison of approximate solution obtained by OHAM with the exact solution obtained by FIM for fractional modified Fornberg–Whitham equation at t=0.2 taking α=0.75

Grahic Jump Location
Fig. 4

Comparison of approximate solution obtained by OHAM with the exact solution obtained by FIM for fractional modified Fornberg–Whitham equation at t=0.4 taking α=0.5

Grahic Jump Location
Fig. 1

Comparison of approximate solution obtained by OHAM with the exact solution obtained by FIM for fractional modified Fornberg–Whitham equation at t=0.1 taking α=1

Grahic Jump Location
Fig. 2

Comparison of approximate solution obtained by OHAM with the exact solution obtained by FIM for fractional modified Fornberg–Whitham equation at t=0.5 taking α=1

Tables

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