init

FOTF Toolbox/fence_shadow.m

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+function fence_shadow(t,f,gam,key)
+% fence_shadow - geometric interpretation of the fractional-order integrals
+%
+%   fence_shadow(t,f,gam,key)
+%   
+%   t - the tine vector
+%   f - the function handle of the original function
+%   gam - the integral order
+%   key - the three types of graphs, as in Igor Podlubny's paper
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 28 March, 2017 
+% Last modified 18 May, 2022 
+   arguments, t(1,:), f, gam(1,1) double
+      key(1,1) {mustBeMember(key,[1,2,3])};
+   end
+   x=t; z=f(x); tn=x(end);
+   switch key
+      case 1, y=(tn^gam-(tn-x).^gam)/gamma(1+gam);
+         axis([minmax(x),minmax(y),minmax(z)]), hold on
+         for i=1:length(x)-1, ii=[i,i,i+1,i+1]; x0=x(ii);
+            z0=[0 z(i:i+1) 0]; y0=[0 0 0 0]; patch(x0,y0,z0,'c')
+            y0=y(ii); patch(x0,y0,z0,'g')
+            x0=[0 0 0 0]; patch(x0,y0,z0,'r')
+         end, view(-37.5000,30)
+      case {2,3}, axis([minmax(x),minmax(z)]), hold on
+         for i=1:length(x)-1, x1=0:0.01:x(i+1);
+            tn=x1(end); y=(tn^gam-(tn-x1).^gam)/gamma(1+gam);
+            if key==2, plot(x1,y);
+            else, z=f(x1); plot(y,z,[y(end),y(end)],[z(end),0]);
+   end, end, end, hold off
+end