init

FOTF Toolbox/caputo9.m

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+function dy=caputo9(y,t,gam,p)
+% caputo9 - O(h^p) Caputo derivative computation function
+%
+%   dy=caputo9(y,t,gam,p)
+%   
+%   y - the samples or function handle of the original function
+%   t - the time vector
+%   gam - the fractional order
+%   p - the order for precision
+%   dy - the Caputo derivative
+
+% 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
+   if strcmp(class(y),'function_handle'), y=y(t); end
+   if gam<0, dy=glfdiff9(y,t,gam,p); return; end
+   h=t(2)-t(1); q=ceil(gam); 
+   r=max(p,q); R=fliplr(vander((sym(0):(r-1))'*h));
+   c=double(R\y(1:r)); u=0; du=0;
+   for i=1:r, u=u+c(i)*t.^(i-1); end
+   if q<r
+      for i=(q+1):p
+         du=du+c(i)*t.^(i-1-gam)*gamma(i)/gamma(i-gam);
+   end, end
+   v=y-u; dv=glfdiff9(v,t,gam,p); dy=dv+du;
+end