Nonlinear Dynamics

, Volume 77, Issue 4, pp 1309–1322

On solutions of two coupled fractional time derivative Hirota equations

Original Paper

DOI: 10.1007/s11071-014-1380-7

Cite this article as:
Bakkyaraj, T. & Sahadevan, R. Nonlinear Dyn (2014) 77: 1309. doi:10.1007/s11071-014-1380-7

Abstract

We consider the well-known nonlinear Hirota equation (NLH) with fractional time derivative and derive its periodic wave solution and approximate analytic solitary wave solution using the homotopy analysis method (HAM). We also apply HAM to two coupled time fractional NLHs and construct their periodic wave solution and approximate solitary wave solution. We observe that the obtained periodic wave solution in both cases can be written in terms of the Mittag–Leffler function when the convergence control parameter \({c}_0\) equals \(-1\). Convergence of the obtained solution is discussed. The derived approximate analytic solution and the effect of time-fractional order \(\alpha \) are shown graphically.

Keywords

Homotopy analysis method Fractional differential and integral operators Mittag–Leffler function Time fractional nonlinear partial differential equations 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Ramanujan Institute for Advanced Study in MathematicsUniversity of MadrasChennaiIndia

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