A novel optimization-based physics-informed neural network scheme for solving fractional differential equations

Nowadays, the study of neural networks is one of the most interesting research topics. In this article, we introduce a novel scheme based on Physics Informed Neural Network (PINN) for solving Fractional Differential Equations (FDEs) in terms of Caputo derivative. We use a trial solution based on the Theory of Functional Connection called the constrained expression to obtain the approximate solution. The training is proposed using the recently introduced average and subtraction-based optimizer algorithm. We implement the proposed algorithm to obtain the approximate solutions of single as well as a system of FDEs. The proposed scheme eliminates the primary drawbacks of the standard PINN. With our scheme, we overcome the choice of additional parameters that affect the convergence.