The Mittag-Leffler relaxation function, , with , plays an important role in the fractional viscoelastic models. The Mittag-Leffler function is an infinite series whose analytic derivatives are unexplored, thus a direct search method based on Powell’s method is introduced to solve the minimization problem of nonlinear least-squares data fitting for Mittag-Leffler relaxation function in this paper. A simple and effective method is provided for the determination of the initial values and an acceleration strategy is proposed for this direct search method. Numerical results show this direct search method is efficient in the parameter estimation of the Mittag-Leffler relaxation function. Furthermore, the acceleration strategy proves to be conducive to improving the computational efficiency of this direct search method.
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