mittagleffler

Mittagleffler is a package for R that implements the Mittag-Leffler function. It uses a f90 code. The original fortran code by Davide Verotta was modified to deal with complex numbers.

How to install

The package

Install the devtools package if you haven't already. Then run:

    library(devtools)
    install_github("emammendes/mittagleffler")

So far the package is only available as source code, so you'll need a functional R build environment (Rtools on Windows, XCode on OS X).

Getting started

    library(mittagleffler)
    lambda <- -1; alpha <- 0.2; 
    t <- (-1)*seq(0,5,0.01)^alpha
    res <- mittagleffler(t,alpha)
    plot(seq(0,5,0.01),res[,1],type="b",xlab="Time",ylab="Amplitude")

A help file is available.

On the fortran code

The original fortran code is provided by Davide Verotta. I have simply modified and updated to accommodate the free form of Fortran 90, to deal with complex numbers and to be part of a R-package. I thank Davide for allowing me to make the code publicly available.

The original fortran code is based on a Matlab function developed by Igor Podlubny and Martin Kacena which was a slightly modified version of Luchko's Mathematica-code and uses the algorithms presented in the paper Computation of the Mittag-Leffler function and its derivatives. Fract. Calc. Appl. Anal. 5(2002), 491-518 by R.Gorenflo, J.Loutchko, and Yu. Luchko

How to reproduce Figure 15 of the paper entitled Computation of the Mittag-Leffler function and its derivatives

    library(mittagleffler)
    alph <- 1.25; 
    t=seq(0,50,0.1)
    y=mittagleffler(t*exp(sqrt(as.complex(-1))*pi),alph)
    plot(t,Re(y[,1]),type="l",xlab="Time",ylab="Amplitude",main=sprintf("alpha=%g and arg=i*pi/4",alph));
    lines(t,Re(y[,2]),type="l",col="red")
    grid(6,5,lty="dotted")
    legend("topright",c("MittagLeffler","Derivative"),lwd=c(2,2),col=c("black","red"),cex=0.6,bty="n",y.intersp=0.6)

emammendes / mittagleffler