% Import the required functions

addpath('functions/'); % Folder containing the fractional derivative functions

% Load training data

load('train_data.mat'); % Replace with your own training data

% Define FONN parameters

N = size(train_data, 2) - 1; % Number of input features

M = 10; % Number of hidden neurons

alpha = 0.8; % Fractional order (0 < alpha < 1)

eta = 0.01; % Learning rate

epochs = 100; % Number of training epochs

% Initialize weight matrices

W = rand(M, N);

b1 = rand(M, 1);

V = rand(1, M);

b2 = rand(1);

% Training loop

for epoch = 1:epochs

for n = 1:size(train_data, 1)

% Forward pass

x = train_data(n, 1:N)';

y = train_data(n, N+1);

% Compute hidden layer output

u = W * x + b1;

z = tanh(u);

% Compute output layer output

v = V * z + b2;

y_hat = v;

% Compute gradients

delta2 = (y_hat - y);

delta1 = V' * delta2 .* sech(u).^2;

% Update weight matrices

W = W - eta * ((RiemannLiouville(alpha, z) * delta1') * x');

V = V - eta * (RiemannLiouville(alpha, delta2) * z');

b1 = b1 - eta * delta1;

b2 = b2 - eta * delta2;

end

% Compute training loss

y_train = predict_fonn(train_data(:, 1:N)', W, b1, V, b2, alpha);

train_loss = mean((y_train - train_data(:, N+1)').^2);

% Display training progress

fprintf('Epoch: %d, Loss: %.6f\n', epoch, train_loss);

end

% Prediction

load('test_data.mat'); % Replace with your own test data

y_test = predict_fonn(test_data(:, 1:N)', W, b1, V, b2, alpha);

% Display test results

fprintf('Test Loss: %.6f\n', mean((y_test - test_data(:, N+1)').^2));

Note: this is fractional order neural network (FONN) implemented in MATLAB using the Riemann-Liouville fractional derivative for training and prediction.

this is a simple implementation and may not be optimized for large-scale datasets. The functions/ folder should contain the Riemann-Liouville fractional derivative functions, such as RiemannLiouville.m and RiemannLiouville_inv.m, which compute the fractional derivatives and their inverse, respectively. These functions can be found in various online resources or custom-implemented based on your specific requirements. Also, make sure to replace the train_data.mat and test_data.mat files with your own training and test data, respectively, in the code above.

Not obtaining graphs dear friend.