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Nonlinear Dynamics

, Volume 85, Issue 1, pp 659–673 | Cite as

Exact solution of certain time fractional nonlinear partial differential equations

  • R. Sahadevan
  • P. Prakash
Original Paper

Abstract

Given a time fractional nonlinear partial differential equation, we show how to derive its exact solution using invariant subspace method. This has been illustrated through time fractional diffusion convection equation, time fractional nonlinear dispersive Boussinesq equation, time fractional reaction diffusion equation of second order, time fractional thin-film equation, and time fractional quadratic wave equation. Also, we explicitly shown that time fractional nonlinear partial differential equations admit more than one invariant subspaces which in turn helps to derive more than one exact solution.

Keywords

Time fractional nonlinear PDEs Invariant subspace method Caputo fractional derivative Laplace transform method  Mittag–Leffler function 

Notes

Acknowledgments

The authors wish to thank the anonymous referees for their constructive suggestions. One of the authors (P.P) would like to thank the University Grants Commission, New Delhi, for providing financial support in the form of Project fellow through Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

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

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