fractional derivative of Ln(x) ?

Is there CODE for fractional derivative of Ln(x) Like in maple

F(x)=Ln(x)

a=alpha

d^a F/dx^a ?

where alpha is a fraction order of the derivative?

[Torsten]

Search the file exchange. E.g.

https://de.mathworks.com/matlabcentral/fileexchange/45982-fractional-derivative

(see below)

Answer 1

[Torsten]

% Sample log between 1 and 4
h = 0.01;
t = 1:h:4;
y = log(t);

% Compute fractional derivatives with different orders
order = 0:0.1:1;
yd    = zeros( length(order), length(t) );

for i=1:length(order)
    yd(i,:) = fgl_deriv( order(i), y, h );
end

plot(t,yd)

function Y = fgl_deriv( a, y, h )
% fgl_deriv
%
%   Computes the fractional derivative of order alpha (a) for the function
%   y sampled on a regular grid with spacing h, using the Grunwald-Letnikov
%   formulation.
%
%   Inputs:
%   a : fractional order
%   y : sampled function
%   h : period of the sampling lattice
%
%   Output:
%   Y : fractional derivative estimate given y
%
%   Note that this implementation is similar to that of Bayat 2007
%   (FileExchange: 13858-fractional-differentiator), and takes the exact
%   same inputs, but uses a vectorized formulation to accelerates the
%   computation in Matlab.
%
%   Copyright 2014 Jonathan Hadida
%   Contact: Jonathan dot hadida [a] dtc.ox.ac.uk

n  = numel(y);
J  = 0:(n-1);
G1 = gamma( J+1 );
G2 = gamma( a+1-J );
s  = (-1) .^ J;

M  = tril( ones(n) );
R  = toeplitz( y(:)' );
T  = meshgrid( (gamma(a+1)/(h^a)) * s ./ (G1.*G2) );
Y  = reshape(sum( R .* M .* T, 2 ), size(y));

end

[esam baker]

thanks