Fitting data using the Mittag-Leffler function

Fitting data using the Mittag-Leffler function.

Two functions are provided for fitting data using the Mittag-Leffler function.

In MLFFIT1.M, just the Mittag-Leffler function in one parameter is used. In MLFFIT2, the Mittag-Leffler function in two parameters multiplied by a power function is used.

Two sample scripts are provided for the illustration of possible use.

These functions require the Mittag-Leffler function (FEX submission 8738); if it is not present, a one-time download is suggested.

This fitting method has been introduced and used in the following articles:

[1] D.Sierociuk, I.Podlubny, I.Petras, "Experimental evidence of variable-order behavior of ladders and nested ladders", IEEE Transactions on Control Systems Technology, 15 February 2012, DOI:10.1109/TCST.2012.2185932, available online at http://dx.doi.org/10.1109/TCST.2012.2185932
(or preprint: http://arxiv.org/abs/1107.2575)

[2] I.Petras, D.Sierociuk, I.Podlubny, "Identification of parameters of a half-order system", IEEE Transactions on Signal Processing, 25 June 2012, DOI:10.1109/TSP.2012.2205920, available online at http://dx.doi.org/10.1109/TSP.2012.2205920

For more information about the Mittag-Leffler function and fractional differential equations (i.e., differential equations containing derivatives of arbitrary real order) see, for example,

[3] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999, ISBN 0125588402.