Attributes of residual neural networks for modeling fractional differential equations

This paper offers a pioneering in-depth exploration of applying residual neural networks to approximate Erdélyi-Kober fractional derivatives and establishes a parameter upper bound for these networks. We validate this method using the variational iteration formula to obtain the exact solution of a differential equation. The resulting structure from the variational iteration method serves as a basis for showcasing how residual neural networks can effectively estimate these equations. Furthermore, we provide illustrative examples to elucidate the application of residual neural networks in solving equations involving Erdélyi-Kober fractional derivatives.