Definition of Caputo fractional order system

Hello,

I want to code this Caputo fractional order dynamics please guide me to do this in matlab. Of course it can be done with simulink but I want to code it.

Thank you in advance for your help.

Answer 1

[Anurag Ojha]

Hi Frashid

In order to code this in MATLAB you can refer to the code attached below,I have taken certain assumptions. Kindly modify it according to your use case:

% Parameters
A = [2 0; -1 -2];
B = [1 0; 0 1];
alpha = 0.9;

% Time vector
t = 0:0.01:10;

% Initial condition
x0 = [0; 0];
u = [1; 1];

% Preallocate memory for state vector
x = zeros(2, length(t));
x(:, 1) = x0;

% Compute dynamics
for i = 2:length(t)
    dt = t(i) - t(i-1);
    dx = A*x(:, i-1) + B*u;
    x(:, i) = x(:, i-1) + dt^alpha*dx;
end

% Plot results
figure;
plot(t, x(1, :), 'b', 'LineWidth', 2);
hold on;
plot(t, x(2, :), 'r', 'LineWidth', 2);
xlabel('Time');
ylabel('State');
legend('x_1', 'x_2');

The code above defines the system matrices A and B, the fractional order alpha, and the time vector t. It then initializes the state vector x and computes the dynamics using a loop. Finally, it plots the results.