Fractional delay differential equations (FDDEs) play a significant role in modeling diverse real-world phenomena characterized by long memory and non-local interactions. Solving FDDEs is a challenging task due to the involvement of non-integer derivatives and their delayed terms. Traditional numerical methods often fail to provide accurate solutions for higher-order FDDEs, necessitating the development of specialized techniques. In this paper, we present an overview of higher-order numerical methods designed specifically for solving FDDEs. We discuss the theoretical background of FDDEs, highlighting their importance in various scientific and engineering applications. Emphasizing the limitations of conventional numerical methods, we delve into the complexities of handling fractional derivatives and delays in FDDEs. To overcome these challenges, we explore several advanced numerical schemes, such as the Adams-Bashforth-Moulton method, the Grünwald-Letnikov discretization technique, and the Caputo difference operator. These methods offer a robust framework to approximate fractional derivatives accurately while efficiently handling the presence of delays in the equations.
Fractional, Integer, Equations, Model, Methods
