Mittag-Leffler function

Calculates the Mittag-Leffler function with desired accuracy.

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)

[YangQuan Chen]

Thanks for the contribution.

[Lingzao zeng]

Excellent.Thanks a lot

[Wang Shaowei]

Thank Prof.Igor Podlubny!

[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!!

[saeed alavi]

thank a lot .

[Enrico Scalas]

It is a nice and useful algorithm.

[mervyn yian]

may i know do u have a complete code for simulating the fractional oscillator........i need in urgently. thanks a lot

[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.

[Eduardo Cuesta]

This function has been useful to me and taking an overview to the code, this seems to be vere, very fine.
Congratulations

[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

[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.

[tamer nabil]

 

[Ivo Petras]

Thanks. It works excellent.

[Haitao Qi]

Thanks. It's the best.

[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.

[udita katugampola]

Thanks for the contribution to the field of Fractional Calculus.

[Roberto Garrappa]

It is a very robust code and is very useful in several applications. An excellent work. It is a reference for practical computation in Fractional Calculus.