init

FOTF Toolbox/glfdiff_mem.m

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+function dy=glfdiff_mem(y,t,gam,L0)
+% glfdiff_mem - evaluation of O(h) GL derivatives with short memory principle 
+%
+%   dy=glfdiff_mem(y,t,gam,L0)
+%
+%   y - the samples of the function handle of the original function
+%   t - the time vector
+%   gam - the fractional order
+%   L0 - the memory length
+%   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), gam(1,1), L0=length(t); end
+   [y,h,n]=fdiffcom(y,t); w=[1,zeros(1,n-1)]; dy(1)=0; 
+   for j=2:L0+1, w(j)=w(j-1)*(1-(gam+1)/(j-1)); end
+   for i=1:n
+      L=min([i,L0]); dy(i,1)=w(1:L)*y(i:-1:i-L+1)/h^gam;
+   end
+end