Mittag-Leffer derivative

版本 1.0.0 (5.2 KB) 作者: Roberto Garrappa
Evaluates integer-order derivatives of the Mittag-Leffler (ML) function
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% Evaluates K-th integer-order derivatives of the Mittag-Leffler (ML) function
%
% E = ML(Z,ALPHA,K) evaluates K-th order derivative of the ML function with
% one parameter ALPHA at each entry of the vector Z; ALPHA must be any real
% and positive scalar value and Z any vector of real or complex values.
%
% E = ML(Z,ALPHA,BETA,K) evaluates K-th order derivative of the ML function
% with two parameters ALPHA and BETA at a scalar argument Z or at each
% entry of Z if Z is a vector; ALPHA must be a real and positive scalar,
% BETA a real scalar value and Z any vector or real or complex values.
%
% Note that the code may result poorly accurate for derivatives of very
% high order K.
%
% TECHNICAL NOTES:
%
% Derivatives of the Mittag-Leffler (ML) function are computed using an
% algorithm that combines a summation formula based on the Prabhakar
% function with a numerical Laplace transform inversion method [2]. This
% combination is guided by the derivatives balancing technique introduced
% in [1]. A detailed description of the algorithm, along with relevant
% properties and applications of ML derivatives, is provided in [3].
%
% If this code is used in research or publications, please cite it as [3].
%
% REFERENCES
%
% [1] 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
%
% [2] R. Garrappa, Numerical Evaluation of two and three parameter
% Mittag-Leffler functions, SIAM Journal of Numerical Analysis, 2015,
% 53(3), 1350-1369.
%
% [3] D.Biolek, R.Garrappa, F.Mainardi, M.Popolizio, Derivatives of
% Mittag-Leffler functions: theory, computation and applications, Nonlinear
% Dynamics, to appear
%
% Please, report any problem or comment to :
% roberto dot garrappa at uniba dot it
%
% Copyright (c) 2025
%
% Authors:
% Roberto Garrappa (University of Bari, Italy)
% roberto dot garrappa at uniba dot it
% Homepage: https://www.dm.uniba.it/members/garrappa
%
%
% Revision: 1.0 - Date: July 29, 2025

引用格式

Roberto Garrappa (2025). Mittag-Leffer derivative (https://ww2.mathworks.cn/matlabcentral/fileexchange/181636-mittag-leffer-derivative), MATLAB Central File Exchange. 检索时间: .

D.Biolek, R.Garrappa, F.Mainardi, M.Popolizio, Derivatives of Mittag-Leffler functions: theory, computation and applications, Nonlinear Dynamics, to appear

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版本 已发布 发行说明
1.0.0