Qualitative analysis of variable‐order fractional differential equations with constant delay

Abstract

This paper presents the computational analysis of fractional differential equations of variable‐order delay systems. To the proposed problem, the existence of solutions is derived using Arzela‐Ascoli theorem, and the Banach fixed point theorem is used for uniqueness results. To investigate and address the computational solutions, Adams‐Bashforth‐Moulton technique is established. To demonstrate the method's efficiency, computational simulations of chaotic behaviors in several one‐dimensional delayed systems with distinct variable orders are employed. The numerical solution of the proposed problem gives high precision approximations.