init

FOTF Toolbox/caputo.m

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+function dy=caputo(y,t,gam,y0,L)
+% caputo - O(h) Caputo derivative computation function
+%
+%   dy=caputo(y,t,alfa,y0,L)
+%   
+%   y - the samples or function handle of the original function
+%   t - the time vector
+%   alpha - the fractional order
+%   y0 - the initial vector of signal and its integer-order derivatives
+%   L0 - the interpolation length
+%   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), gam(1,1), y0, L(1,1)=10, end
+   dy=glfdiff(y,t,gam);
+   if gam>0, q=ceil(gam); if gam<=1, y0=y(1); end
+      for k=0:q-1, dy=dy-y0(k+1)*t.^(k-gam)./gamma(k+1-gam); end
+      yy1=interp1(t(L+1:end),dy(L+1:end),t(1:L),'spline');
+      dy(1:L)=yy1;
+   end
+end