Zener Viscoelastic Model Characterization Using the Atangana-Baleanu Fractional Derivative

Abstract

The continuous search for new mathematical models that accurately represent real-world phenomena is a constant goal in the scientific community. To achieve this objective, the complexity of a large number of mathematical models has increased, such that certain considerations or restrictions and the use of numerical methods with greater computational requirements are required for their solution. For this, theories such as fractional calculus have been used, which have demonstrated an adequate characterization of physical phenomena, mainly in the area of biomechanics. However, there is no unique definition of the derivative concept, as in the case of integers, because it is a “new theory”. In this article, the kernel of the Atangana-Baleanu fractional derivative is used, which satisfies the most common properties of the classical derivative, and addresses the existing problem when considering initial conditions of the model, which in biomechanics is associated with material memory.