Multilayered neural network for power series-based approximation of fractional delay differential equations

This paper trains a multilayered neural network (MLNN) for solving fractional delay differential equations (FDDEs), including nonlinear and singular types. The proposed methodology involves replacing the unknown functions in the equations with a truncated power series expansion. Subsequently, a collection of algebraic equations is solved utilizing an iterative minimization technique that leverages the capabilities of the MLNN architecture. The outcomes demonstrate that the MLNN architecture provides the required accuracy and strong stability compared to several numerical methods.