Numerical Approach to Describe Fractional Viscoelasticity

Fractional viscoelasticity introduces a new approach to describe viscoelastic materials using derivatives and integrals of noninteger order.The main disadvantage of this approach is its use in numerical applications because, compared to standard integer-order derivatives, the numerical approximation of the fractional derivative is based on all of the nodal values from the previous time steps while each of these values has a different weight in the computation.For this reason, the usability for large-scale problems is limited because of high memory and computing time requirements.This paper presents several approaches how to deal with this problem by introducing approximation of the fractional derivative which uses only reduced number of previous values.