Mathematical fractional Zeeman model for describing cardiac contractions

he article proposes a fundamentally new generalization of the previously known mathematical Zeeman model of heart contractions due to electrochemical action. This generalization is due to the presence of heredity effects in the oscillatory system, which indicate that it can store information about its previous states. From the mathematical point of view, the property of heredity can be described using integrodifferential equations of the Volterra type with power difference kernels or using fractional derivatives. In the article, fractional differentiation operators in the sense of Gerasimov-Caputo were introduced into the Zeeman model equations, as well as the characteristic time for matching dimensions in the model equations. The resulting mathematical fractional Zeeman model was studied due to its nonlinearity using numerical methods – a nonlocal finite-difference scheme. The numerical algorithm was implemented in Python in the PyCharm 2024.1 environment, which implemented the ability to visualize calculations using oscillograms and phase trajectories. The interpretation of the modeling results was carried out.