Matlab caputo fractional code
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Help please, im in need for a code matlab fractional i found this code but it dosnt work, if you have in idea please chare with me
% SIR fractional system using Caputo fractional derivative
clear all; close all; clc;
% Parameters
alpha = 0.8; % order of the fractional derivative
beta = 0.4; % infection rate
gamma = 0.2; % recovery rate
N = 1000; % total population
I0 = 1; % initial number of infected individuals
R0 = 0; % initial number of recovered individuals
S0 = N - I0 - R0;% initial number of susceptible individuals
tend = 10; % end time
dt = 0.01; % time step
% Initialization
t = 0:dt:tend;
Nt = length(t);
S = zeros(1, Nt);
I = zeros(1, Nt);
R = zeros(1, Nt);
S(1) = S0;
I(1) = I0;
R(1) = R0;
% Main loop
for n = 1:Nt-1
% Compute fractional derivatives using the Caputo derivative
DalphaS = CaputoDerivative(S(n),alpha,t(n),dt);
DalphaI = CaputoDerivative(I(n),alpha,t(n),dt);
DalphaR = CaputoDerivative(R(n),alpha,t(n),dt);
% Compute derivatives using standard differential equations
dSdt = -beta*S(n)*DalphaI/N;
dIdt = beta*S(n)*DalphaI/N - gamma*DalphaI;
dRdt = gamma*DalphaI;
% Update variables
S(n+1) = S(n) + dt*dSdt;
I(n+1) = I(n) + dt*dIdt;
R(n+1) = R(n) + dt*dRdt;
end
% Plot results
plot(t, S, 'r', t, I, 'g', t, R, 'b');
legend('Susceptible', 'Infected', 'Recovered');
xlabel('Time');
ylabel('Population');
title('Fractional SIR System using Caputo Derivative');
grid on;
% Caputo derivative function
function y = CaputoDerivative(f,alpha,t,dt)
% Computes the Caputo fractional derivative of order alpha
% f: function to differentiate
% alpha: order of the fractional derivative
% t: current time
% dt: time step
% Compute the intermediate values for the Caputo derivative
N = length(f);
m = floor(alpha);
A = zeros(N,N-m);
for k = m:N-1
A(k+1-m,k+1-m:k) = dt.^(-(0:k-m)).*gamma(k-m+1)./gamma(k+2-m).*(-1).^(0:k-m);
end
% Compute the Caputo derivative
y = A*f(m+1:N)';
end
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2023-4-20
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