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Fitting data using the Mittag-Leffler function

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Fitting data using the Mittag-Leffler function


Igor Podlubny (view profile)


11 Jul 2011 (Updated )

Fitting data using the Mittag-Leffler function.

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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
(or preprint:

[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

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.

MATLAB release MATLAB 7.8 (R2009a)
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Comments and Ratings (1)
02 Dec 2014 Caibin Zeng

11 Jul 2011 1.1

Missing lines of code added.

14 Jul 2011 1.2

Added references.

19 Jul 2011 1.4

Demo files made m-publishable, and PDF outputs of demos are added. Screenshot updated.

02 Apr 2012 1.5

Added a reference to the journal paper.

27 Jun 2012 1.6

Updated description.

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