# American Institute of Mathematical Sciences

## Analysis of the Fitzhugh Nagumo model with a new numerical scheme

 Department of Mathematics, Gyan Ganga Institute of Technology and Sciences, Near Tilwara Ghat, Jabalpur, Pin-482003, M.P., India

Received  May 2018 Revised  May 2018 Published  March 2019

The model describing a prototype of an excitable system was extended using the newly established concept of fractional differential operators with non-local and non-singular kernel in this paper. We presented a detailed discussion underpinning the well-poseness of the extended model. Due to the non-linearity of the modified model, we solved it using a newly established numerical scheme for partial differential equations that combines the fundamental theorem of fractional calculus, the Laplace transform and the Lagrange interpolation approximation. We presented some numerical simulations that, of course reflect asymptotically the real world observed behaviors.

Citation: Jyoti Mishra. Analysis of the Fitzhugh Nagumo model with a new numerical scheme. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020044
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Numerical solution for $\alpha = 0.15$
Numerical solution for the value $\alpha = 0.35$
Numerical solution for the value $\alpha = 0.70$
Numerical solution for the value $\alpha = 0.75$
Numerical solution value $\alpha = 0.95$
Numerical solution value $\alpha = 1$
Contour plot value $\alpha = 0.15$
Contour plot value $\alpha = 0.35$
Contour plot for $\alpha = 0.75$
Contourplot for $\alpha = 1$
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