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A comparative study on the analytic solutions of fractional coupled sine–Gordon equations by using two reliable methods

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  • Saha Ray, S.
  • Sahoo, S.

Abstract

In this paper modified homotopy analysis method (MHAM) and homotopy perturbation transform method (HPTM) have been implemented for solving time fractional coupled sine–Gordon equations. We consider fractional coupled sine–Gordon equations which models one-dimensional nonlinear wave processes in two-component media. The results obtained by modified homotopy analysis method (MHAM) and homotopy perturbation transform method (HPTM) are then compared with the modified decomposition method (MDM). By using an initial value system, the numerical solutions of coupled sine–Gordon equations have been represented graphically. Here we obtain the solution of fractional coupled sine–Gordon (S–G) equations, which is obtained by replacing the time derivatives with a fractional derivatives of order α∈(1,2] and β∈(1,2]. The fractional derivatives here are described in Caputo sense.

Suggested Citation

  • Saha Ray, S. & Sahoo, S., 2015. "A comparative study on the analytic solutions of fractional coupled sine–Gordon equations by using two reliable methods," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 72-82.
    • Handle: RePEc:eee:apmaco:v:253:y:2015:i:c:p:72-82
    DOI: 10.1016/j.amc.2014.12.052
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