A novel lagrange functional link neural network for solving variable-order fractional time-varying delay differential equations: a comparison with multilayer perceptron neural networks

This study introduces a novel functional link neural network and explores the associated theorems for a class of nonlinear differential equations with fractional variable-order and time-varying delays. Lagrange polynomials, known for their efficiency in solving fractional calculus problems, are utilized as the neuro-solutions within the neural network structure. For an efficient learning process in artificial neural networks, appropriate activation functions play a crucial role. To handle the fractional derivative of variable-order and time-varying delays, it is essential to select the right activation function. Hence, numerical simulations are conducted to determine the optimal activation function for these equations. The training of the neural network is done using a modified Newton–Raphson method instead of the traditional supervised learning methods. As a result, the proposed functional link neural network provides more accurate results compared to conventional neural networks like the multilayer perceptron.