init

FOTF Toolbox/glfdiff9.m

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+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