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.
