On the conservation laws and invariant analysis for time-fractional coupled Fitzhugh-Nagumo equations using the Lie symmetry analysis
Kalinga Institute of Industrial Technology, Department of Mathematics, 751024, Bhubaneswar, Odisha, India
2 National Institute of Technology, Department of Mathematics, 769008, Rourkela, India
* e-mail: email@example.com
Accepted: 30 November 2018
Published online: 28 February 2019
In this paper, the application of the fractional Lie symmetry method has been used for similarity reduction of the nonlinear fractional reaction-diffusion model. Also, it has been utilized for analyzing the conservation laws of the nonlinear fractional reaction-diffusion model viz. time fractional coupled Fitzhugh-Nagumo (FHN) equations. Foremost, the proposed method has been utilized to generate the infinitesimal generators for the time fractional coupled FHN equations. Then, with the help of Erdélyi-Kober differential operators, the fractional coupled differential equations have been reduced to fractional ordinary differential equations. Here, the Erdélyi-Kober differential operators have been defined via the Riemann-Liouville derivative. The new conserved vectors have been derived with the help of the proposed conservation theorem and formal Lagrangian.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019