A Robust Higher-Order Scheme for Fractional Delay Differential Equations Involving Caputo Derivative

This article considers nonlinear fractional delay differential equations involving Caputo’s fractional derivative of order \(\alpha \in (0,1)\) $\alpha \in (0,1)$ . We focus on designing a robust numerical algorithm of order \(O(h^{4-\alpha })\) $O(h^{4-\alpha })$ . To achieve this, we developed a higher-order interpolation-based approximation for Caputo’s derivative, which enables us to construct a robust numerical scheme for the considered problem. Furthermore, we discuss the stability and error analysis of the proposed higher-order scheme. Finally, numerous examples, including real-life applications, are evaluated to demonstrate the computational efficiency of the proposed algorithm.