Semi-analytical Solution of Linear and Nonlinear Fractional Delay Differential Equations via The Legendre Collocation Method

Abstract

Abstract The fractional delay differential equation (FDDE) exhibits an adaptable framework for modeling and analyzing systems where the traditional integer-order model falls short. Its ability to mingle fractional-order dynamics and delay effects makes it a significant tool across distinct fields. The key objective of this article is to manifest the significance of solving fractional delay differential equations numerically by utilizing the Legendre collocation method. The FDDE has been reduced to a system of algebraic equations. Interpretative numerical examples have been demonstrated to display the effectiveness and preciseness of the potential method for solving FDDE. The prospective method has been verified via error analysis and comparison with other methods.