A Novel Numerical Treatment for Solving Fractional Order Delay Integro-Differential Algebraic Equations Using Fractional Physics-Informed Neural Networks Method

In this paper, we extend Physics-Informed Neural Networks (PINNs), to solve fractional order delay integro-differential algebraic equations. In the proposed approach, we employ the standard feedforward neural networks (NNs) with the delay integro-differential algebraic equations are straightforward encoded into the NN using fractional order differentiation. While the sum of the mean squared fractional order delay integro differential algebraic equations-residuals and the mean squared error in initial conditions is minimized with respect to the NN parameters.