Finite difference <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si0125.svg"><mml:mi>β</mml:mi></mml:math>-fractional approach for solving the time-fractional FitzHugh–Nagumo equation

This study presents a numerical approach for addressing the time-fractional FitzHugh–Nagumo (TFFHN) equation, a key equation in physics. The method integrates β-fractional derivatives s with the finite difference technique. Stability analysis confirms that the proposed method is conditionally stable. Numerical experiments demonstrate its effectiveness, outperforming the cubic B-spline method regarding norm errors. The experimental order of convergence is also presented, highlighting the accuracy and efficiency of the approach, and emphasizing its potential for solving time-fractional differential equations across various physical applications.