Determinación del orden fraccional en el modelo Zener para caracterizar los efectos biomecánicos ocasionados por el flujo sanguíneo

The main purpose of this publication is the proper determination of the fractional order at the Zener viscoelastic model's and the analysis of the implications derived from the accuracy in obtaining this. The procedure is performed using the numerical method of Levenberg-Marquardt from values reported in the literature. The parameters used are obtained from an artery segment using a stress relaxation test. After determining the fractional order is proceeded to find the model solution using, the function of Mittag-Leffler with two parameters and the convolution operation in order to compare the behavior of the fractional model vs the integer order and identify their key differences. The displacements present on the artery are obtained, under the stimulus of a normal blood pulse and two dissimilar, simulating the effect in blood flow caused by an arrhythmia and by mechanical ventilation process. Finally the dynamic response from the pulses is analyzed using the convolution operation and Gauss Kronrod numeric method, where the solution's accuracy obtained by the fractional model is observed, an compared with the integer order model.