doi: 10.1685/journal.caim.487

Nonlinear time-fractional dispersive equations

Piero Artale Harris, Roberto Garra

Abstract


In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional partial differential equations by separating variables. We first consider a third order time-fractional NDE that admits a four-dimensional invariant subspace and we find a similarity solution. We also study a fifth order NDE. In this last case we find a solution involving Mittag-Leffler functions. We finally observe that the invariant subspace method permits to find explicit solutions for a wide class of nonlinear dispersive time-fractional equations.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


Creative Commons License

This work is licensed under a Creative Commons Attribution NonCommercial NoDerivs 3.0 License.

Communications in Applied and Industrial Mathematics
ISSN: 2038-0909