Abstract: Functions of Mittag-Leffler(M-L) type play a special role in the fractional order viscoelastic theory. However, this function converges very slowly and it will likely result in divergence in numerical evaluation. The convergence criterion and the evaluation of M-L functions is discussed. When applying fractional Maxwell model to the stress relaxation, the parameters determined by using the asymptotic solutions of M-L functions are not correct to describe the relaxation process. A method combining genetic algorithm and conjugated gradient was proposed to optimize the model parameters. And the fractional Maxwell model based on the optimized parameters can be used to simulate viscoelastic relaxation process very well.

Key words: Fractional Maxwell model, Mittag-Leffler function, Viscoelasticity, Stress relaxation