Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system

Abstract This paper delves into the dynamical analysis, chaos control, Mittag–Leffler boundedness (MLB), and forecasting a fractional-order financial risk (FOFR) system through an absolute function term. To this end, the FOFR system is first proposed, and the adomian decomposition method (ADM) is employed to resolve this fractional-order system. The stability of equilibrium points and the corresponding control schemes are assessed, and several classical tools such as Lyapunov exponents (LE), bifurcation diagrams, complexity analysis (CA), and 0–1 test are further extended to analyze the dynamical behaviors of FOFR. Then the global Mittag–Leffler attractive set (MLAS) and Mittag–Leffler positive invariant set (MLPIS) for the proposed financial risk (FR) system are discussed. Finally, a proficient reservoir-computing (RC) method is applied to forecast the temporal evolution of the complex dynamics for the proposed system, and some simulations are carried out to show the effectiveness and feasibility of the present scheme.