Original Research Article

Article volume = 2022 and issue = 1

Pages: 55–61

Article publication Date: November 21, 2022

# An Accurate Approach to The Simulation of Nonlinear Generalized Fractional Fisher Equation

#### Hamid Mesgarani and Yones Esmaeelzade Aghdam

Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-136, I.R.Iran.

##### Abstract:

The Fisher dissemination exchange properties, as well as reaction from characteristics, make the non-linear model. The nonlinear fractional Fisher model shows up in practical physical circumstances like ultra-slow kinetics, Brownian movement of particles, anomalous diffusion, polymerases of Ribonucleic acid, deoxyribonucleic acid, continuous irregular activity, and arrangement of wave kinds. The paper considered the strategy based on the Chebyshev polynomials to get the numerical method to solve the nonlinear generalized fractional Fisher equation. The numerical scheme is developed in the following manners: at first, the semi-discrete is constructed in the temporal sense based on a linear interpolation with accuracy order $\delta ^2 t$, and secondly, the full discrete of the model is investigated. Moreover, the unconditional stability and convergence order are investigated via the numerical results. For getting of the full-discrete scheme, the spatial derivative is approched based on the shifted Chebyshev basis. In addition, the adequacy and legitimacy of the proposed modern are illustrated by means of two test.

##### Keywords:

Fisher model, Nonlinear generalized fractional Fisher equation, Chebyshev polynomials, Collocation method.

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