ARTIFICIAL NEURAL NETWORK TECHNIQUE FOR SOLVING ONE-DIMENSIONAL FRACTIONAL RAYLEIGH–STOCKES EQUATION

This paper employs an artificial neural network (ANN) method to achieve an approximate solution [Formula: see text] of the one-dimensional fractional Rayleigh–Stokes equation with boundary and initial conditions. ANN is a machine learning branch that aims to minimize the loss function, which closely approaches the solution of mathematics equations. By combining the ANN output with the initial and boundary conditions, we can achieve an adequate approximation for this fractional equation. The study utilizes a multi-layer feed-forward neural network algorithm and error backpropagation method with unsupervised learning to minimize the loss function and parameter alteration (weights and biases). The accuracy and effectiveness of the ANN technique were demonstrated through several examples. This method can approximate solutions of the Rayleigh–Stokes equation for more than 10,000 points with considerable accuracy in a short time. A comparison of the results achieved with other existing techniques indicates that the ANN method provides a more appropriate approximation.