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Research Papers

Traveling Wave Solutions to Riesz Time-Fractional Camassa–Holm Equation in Modeling for Shallow-Water Waves

[+] Author and Article Information
S. Saha Ray

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

S. Sahoo

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

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 22, 2014; final manuscript received February 4, 2015; published online June 25, 2015. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 10(6), 061026 (Nov 01, 2015) (5 pages) Paper No: CND-14-1296; doi: 10.1115/1.4029800 History: Received November 22, 2014; Revised February 04, 2015; Online June 25, 2015

In the present paper, we construct the analytical exact solutions of a nonlinear evolution equation in mathematical physics, viz., Riesz time-fractional Camassa–Holm (CH) equation by modified homotopy analysis method (MHAM). As a result, new types of solutions are obtained. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method. The main aim of this paper is to employ a new approach, which enables us successful and efficient derivation of the analytical solutions for the Riesz time-fractional CH equation.

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Figures

Grahic Jump Location
Fig. 1

The ℏ-curve for partial derivatives of u(x,t) at (0,0) for the MHAM solution

Grahic Jump Location
Fig. 2

(a) The MHAM method traveling wave solution for u(x,t) and (b) corresponding 2D solution for u(x,t) when t=1

Grahic Jump Location
Fig. 3

(a) The MHAM method traveling wave solution for u(x,t) and (b) corresponding 2D solution for u(x,t) when t=1

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