FractionOrderSystem/FOTF Toolbox/glfdiff9.m

27 lines
928 B
Matlab

function dy=glfdiff9(y,t,gam,p)
% glfdiff9 - evaluation of O(h^p) GL derivatives, recommended
%
% dy=glfdiff9(y,t,gam,p)
%
% y - the samples of the function handle of the original function
% t - the time vector
% gam - the fractional order
% p - the order for the precision setting
% dy - the fractional-order derivatives, or integrals if gam<0
% Copyright (c) Dingyu Xue, Northeastern University, China
% Last modified 28 March, 2017
% Last modified 18 May, 2022
arguments, y(:,1), t(:,1) double, gam(1,1) double
p(1,1){mustBePositiveInteger}=5
end
[y,h,n]=fdiffcom(y,t); u=0; du=0; r=(0:p)*h;
R=sym(fliplr(vander(r))); c=double(R)\y(1:p+1);
for i=1:p+1, u=u+c(i)*t.^(i-1);
du=du+c(i)*t.^(i-1-gam)*gamma(i)/gamma(i-gam);
end
v=y-u; g=double(genfunc(p)); w=get_vecw(gam,n,g);
for i=1:n, dv(i,1)=w(1:i)*v(i:-1:1)/h^gam; end
dy=dv+du; if abs(y(1))<1e-10, dy(1)=0; end
end