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Mittag-Leffler function with matrix arguments

version (12.8 KB) by Roberto Garrappa
Evaluate the Mittag-Leffler function with two parameters when the argument is a square matrix


Updated 02 Mar 2018

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Evaluate the Mittag-Leffler (ML) function with two parameters ALPHA and BETA of 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. If the second parameter BETA is missing, it is assumed BETA=1.
The ML function on the matrix argument A is evaluated by exploiting the Schur-Parlett algorithm and evaluating derivative of the scalar ML function by combining, by means of the derivatives balancing technique studied in [1], Taylor series, a summation formula based on the Prabhakar function and the numerical inversion of the Laplace transform obtained after generalizing the algorithm described in [2]. For more details users are referred to [1]. Please, cite this code as [1].

[1] R. Garrappa and M. Popolizio, Computing the matrix MittagLeffler function with applications to fractional calculus, submitted
[2] R. Garrappa, Numerical Evaluation of two and three parameter Mittag-Leffler functions, SIAM Journal of Numerical Analysis, 2015, 53(3), 1350-1369.

Comments and Ratings (2)

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

Inspired by: The Mittag-Leffler function