https://doi.org/10.1140/epjp/i2019-12440-6
Regular Article
On the conservation laws and invariant analysis for time-fractional coupled Fitzhugh-Nagumo equations using the Lie symmetry analysis
1
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: santanusaharay@yahoo.com
Received:
18
November
2017
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
