Fractional Volterra integral equations: a neural network approach

Fractional calculus has recently gained increasing interest in the economic and financial literature. As for economic models, economic growth has been modeled using a state space representation of fractional derivatives. These kinds of equations do not allow closed-form solutions and therefore require appropriate numerical methods to obtain accurate approximations of the solutions. For this reason, in this paper, we propose an approach based on Physics Informed Neural Network to solve Volterra fractional-order integral equations. Some numerical experiments show the accuracy of the suggested algorithm.