init

FOTF Toolbox/fode_caputo0.m

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+function [y,z]=fode_caputo0(a,na,b,nb,y0,u,t)
+% fode_caputo0 -  simple Caputo FODE solver with nonzero initial conditions
+%
+%   [y,z]=fode_caputo0(a,na,b,nb,y0,u,t)
+%   
+%   a,na,b,nb - coefficients/order vectors of numerator and denominator
+%   y0 - the initial vector of the output and its integer-order derivatives
+%   u - the samples of the input signal
+%   t - the time vector, corresponding to u
+%   y - the solutions of the Caputo equation, with O(h)
+%   z - the solution portion for zero initial condition ones
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 28 March, 2017 
+% Last modified 18 May, 2022 
+   arguments
+      a(1,:), na(1,:), b(1,:), nb(1,:), y0(:,1), u(:,1), t(:,1) 
+   end
+   h=t(2)-t(1); T=0; P=0; U=0;
+   for i=1:length(y0), T=T+y0(i)*t.^(i-1)/gamma(i); end
+   for i=1:length(na), P=P+a(i)*caputo9(T,t,na(i),5); end
+   for i=1:length(nb), U=U+b(i)*caputo9(u,t,nb(i),5); end
+   z=fode_sol(a,na,1,0,U-P.',t); y=z+T;
+end