Artificial Neural Network Technique for Solving Variable Order Fractional Integro-Differential Algebraic Equations

Abstract

In this paper, we will use an artificial neural network (ANN) to solve the variable order fractional integro-differential algebraic equations (VFIDAEs), which is a three-layer feed-forward neural architecture that is formed and trained using a backpropagation unsupervised learning algorithm based on the gradient descent rule for minimizing the error function and parameter modification (weights and biases). When we combine the initial conditions with the ANN output, we get a good approximation of the VFIDAE solution. Finally, the analysis is complemented by two numerical examples that demonstrate the method capability. The collected results show that the suggested strategy is quite successful, resulting in superior approximations in these cases.