The role of residual neural networks for advancing fractional differential equations

Abstract

This study provides the first comprehensive demonstration of how to utilise ResNets to estimate a family of generalized Caputo-type fractional differential equations and their solutions, and how to limit the quantity of parameters present in these ResNets. The basis of our evidence is the variational iteration method. It determines the differential equation's exact solution with the use of the variational iteration method. Then it shows how to estimate these equations using residual neural networks, using the structure produced by the variational iteration method ($\mathit{VIM}$).