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Mittag-Leffler function

17 Oct 2005 (Updated 25 Mar 2009)

Code covered by the BSD License

Calculates the Mittag-Leffler function with desired accuracy.

File Information

Description

This is a MATLAB routine for evaluating the Mittag-Leffler function with two parameters (sometimes also called generalized exponential function).

The Mittag-Leffler function with two parameters plays an important role and appears frequently in solutions of fractional differential equations (i.e. differential equations containing fractional derivatives).

USAGE:
MLF(alpha,beta,Z,P) is the Mittag-Leffler function E_{alpha,beta}(Z) evaluated with accuracy 10^(-P) for each element of Z.

Update 2009-03-25:
(1) Now Z can also be a two-dimensional array.
(2) Addressed the issue reported by Li Jackie. It was caused by rounding errors during computations.

MATLAB release

MATLAB 6.0 (R12)

Tags for This File
Everyone's Tags	fractional calculus(2), mittagleffler function(2), special functions(2)
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Comments and Ratings (15)
17 Oct 2005	YangQuan Chen	Thanks for the contribution.
12 Nov 2005	Lingzao zeng	Excellent.Thanks a lot
21 Nov 2005	Wang Shaowei	Thank Prof.Igor Podlubny!
21 Dec 2005	Alvaro Cartea	It is great to have someone like Podlubny put the code out. This saves people in the field a great deal of time!!
15 Feb 2006	saeed alavi	thank a lot .
16 Feb 2006	Enrico Scalas	It is a nice and useful algorithm.
29 Sep 2006	mervyn yian	may i know do u have a complete code for simulating the fractional oscillator........i need in urgently. thanks a lot
09 Oct 2006	Vamsi Krishna	That was very very helpful sir.Please let me know the algorithm you have used or any reference paper which contains the properties you have used.Please let me know if you have written the code for MLF with three parameters.
23 Mar 2007	Eduardo Cuesta	This function has been useful to me and taking an overview to the code, this seems to be vere, very fine. Congratulations
25 Apr 2007	Assabaa Mohamed	can you send me a complete code for simulating the fractional oscillator,I need it urgently to confirm an idea. thanks a lot
14 Mar 2008	Li Jackie	Why there exists complex value in the numerical result of the Mittag-Leffler function when the variable (named z) is real? Recently I used the programe MLF.m to compute the Mittag-Leffler function in Matlab. But I had a problem that there existed complex value in the numerical result of the Mittag-Leffler function. Since the interval of z (variable of function) I setted is a subset of real space, I can't explain why appearence of complex value of Mittag-Leffler function. Could someone give me some advice? Hope it will not delay you too much time. Thanks.
10 Oct 2008	tamer nabil
25 Mar 2009	Ivo Petras	Thanks. It works excellent.
12 Apr 2009	Haitao Qi	Thanks. It's the best.
20 Nov 2009	Maxwelldemon ??	The code is very very helpful. Thanks a lot. However, there exists a problem: When 1<alfa<2, beta>1, the returned value has a jump when the variable z is around -170. When alfa=1.5, I tried beta=1.5, 2.5, 3.5, the jump always happens around -170. Furthermore, in the code, I can't find computations for the case 1<alfa<2, when z>floor(20/(2.1-alfa)^(5.5-2*alfa)). I will be very thankful for any advice.

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Updates
18 Oct 2005	Keywords were truncated by the system during file submission. One can enter many characters in the 'Keywords' field of the file submission form, but it appears that the FileExchange system accepts only first 70 characters in the "Keywords" field.
19 Jul 2006	minor update (thanks to Dominik Sierociuk for his feedback)
25 Mar 2009	(1) Now Z can also be a two-dimensional array. (2) Addressed the issue reported by Li Jackie. It was caused by rounding errors during computations.

Tag Activity for this File
Tag	Applied By	Date/Time
mittagleffler function	Igor Podlubny	22 Oct 2008 08:03:09
special functions	Igor Podlubny	22 Oct 2008 08:03:09
fractional calculus	Igor Podlubny	22 Oct 2008 08:03:09
special functions	Jagannath	01 Jun 2009 20:41:19
fractional calculus	Maxwelldemon ??	21 Nov 2009 02:07:30
mittagleffler function	Maxwelldemon ??	21 Nov 2009 02:07:32

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