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## Mittag-Leffler function with matrix arguments

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Evaluate the Mittag-Leffler function with one or two parameters at square matrix arguments

Updated 20 Oct 2020

This MATLAB functions evaluates the Mittag-Leffler (ML) function with two parameters ALPHA and BETA at the square matrix argument A

E = ML(A,ALPHA,BETA) evaluates the ML function with two parameters ALPHA and BETA at the square matrix A argument; ALPHA must be any real and positive scalar, BETA any real scalar and A any real or complex square matrix.

E = ML(A,ALPHA) evaluates the ML function with one parameter ALPHA at the square matrix A argument; ALPHA must be any real and positive scalar and A any real or complex square matrix.

REFERENCES

 R. Garrappa and M. Popolizio, Computing the matrix Mittag–Leffler function with applications to fractional calculus, Journal of Scientific Computing, 2018, 17(1), 129-153 - doi: https://doi.org/10.1007/s10915-018-0699-5

 R. Garrappa, Numerical Evaluation of two and three parameter Mittag-Leffler functions, SIAM Journal of Numerical Analysis, 2015, 53(3), 1350-1369.

### Cite As

R. Garrappa and M. Popolizio, Computing the matrix Mittag–Leffler function with applications to fractional calculus, Journal of Scientific Computing, 2018, 17(1), 129-153

benyettou kamel

To Roberto Garrappa thank you

Roberto Garrappa

To Benyettou Kamel: this code evaluate numerically, and not symbolically, the ML function with matrix argument. The input must be therefore, necessarily, a constant matrix.

benyettou kamel

hellows, for example, if we have alpha=beta=1 and A=[t 0 0;0 t 0;0 0 t] ( A matrix depend to t ) matlab give :??? Error using ==> funm at 150
First input must be a single or double square matrix.

Error in ==> ml_matrix at 89
E = funm(A,mldr) ;
? what is the problem in this case ?

benyettou kamel

Junsheng Duan

Ivan Matychyn

##### MATLAB Release Compatibility
Created with R2014a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux