Analytical and Numerical Study of a New Class of Fractional Delay Differential Equations with Caputo and Riemann–Liouville Derivatives

Abstract

We study the analytical properties of the proposed model, focusing on the ex- istence and uniqueness of solutions. By applying Picard’s iterative method under relaxed Lipschitz conditions on the nonlinear functions, we establish results without requiring classical contraction assumptions. In addition, we develop a numerical scheme based on integral approximations and demonstrate its convergence under the same set of assumptions.

Our results contribute to the theoretical and numerical understanding of frac- tional systems with delay, offering a robust approach to modeling real-world phe- nomena with non-local, nonlinear, and memory-dependent dynamics.