Supply Chain Management (SCM) is a critical business function that involves the planning, coordination,
and control of the flow of goods, information, and finances as they move from the
manufacturer to the wholesaler to the retailer and finally to the end customer. SCM is a holistic
approach to managing the entire process of delivering products or services to consumers. In this
study, we will enhance the findings as outlined in Anne et al. (2009). While certain attributes of
these systems will have been investigated, numerous aspects of these systems will still require
further scrutiny. This calls for additional research studies on these systems. This paper examines a
Fractional-Order Supply Chain Management (FOSCM) model utilizing the Adomian Decomposition
Method (ADM) and explores qualitative aspects through an approach that addresses existence
and uniqueness. By using Arzel`a–Ascoli’s principle, this system proves that the Caputo
FOSCM model has at least one solution. Furthermore, we investigate the dynamics of the system
by using the Lyapunov Exponent (LE), Bifurcation Diagram (BD), Complexity Analysis (CA) and
0–1 test. Finally, we introduce the control for FOSCM model using the Linear Feedback Control
(LFC) method. We verify the correctness of our analysis by using numerical simulations.