## Application of Gegenbauer Wavelet Method on Initial Value Problem of Fractional Order Fitz Hugh-Nagumo Equation

Jie Yang *

School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, PR China.

Yue Zhou

School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, PR China.

*Author to whom correspondence should be addressed.

### Abstract

This paper provides a detailed introduction to the fractional order differentials and the matrix operations of the Gegenbauer wavelet method for solving fractional order differential equations. By comparing the derived trigonometric fractional order differential form solution with the reconstructed Gegenbauer wavelet solution in exploring the initial value problem of the fractional order FitzHugh-Nagumo equation, this paper not only verifies the suitability of the defined fractional order differential form solution for numerical computations but also highlights the high accuracy of the Gegenbauer wavelet method in solving fractional order differential equations. Furthermore, by comparing the exact solution with the reconstructed solution using the Gegenbauer wavelet method, it is concluded that the synchronization rate between neurons in the fractional order FitzHugh-Nagumo model is faster than the corresponding integer-order synchronization rate.

Keywords: Fractional calculus, FitzHugh-Nagumo equation, Gegenbauer wavelet, Mittag-Leffler function

#### How to Cite

*Asian Journal of Mathematics and Computer Research*,

*30*(4), 83–101. https://doi.org/10.56557/ajomcor/2023/v30i48417

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