Existence, Uniqueness and Error Analysis of Variable-Order Fractional Lorenz System with Various Type of Delays

This paper examines the variable-order fractional Lorenz system with distinct types of delays. The application of the Arzela–Ascoli theorem is made to prove the existence of solutions for the given problem, while the Banach fixed point theorem is employed to derive the uniqueness results. The utilization of the Adams–Bashforth–Moulton technique facilitates the exploration and resolution of the approximation solution, complemented by a thorough error analysis of particular approaches. The computational simulations showing chaotic behaviors in various delayed systems with different variable orders demonstrate the effectiveness of the approach.