Fractional dynamical behavior of electrical activity in a model of pancreatic β-cells

The electrical activity of a three dimensional fractional-order model of pancreatic β-cells is numerically studied. The dynamics of the model is understood through the Adams-Bashforth-Moulton predictor corrector scheme, which is a time-domain approach. By considering both integer-order and fractional-order models, we highlight some differences in their dynamics characteristics. It is shown that the fractional model can give rise to chaotic dynamics due to the existence of a Smale horseshoe. Some behaviors related with diabetes mellitus are also reported. The fractional model gets closer to the real biological behavior, thus provides motivation in modeling biological systems with fractional order derivatives.