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