Sukono et al. Advances in Difference Equations ( 2020) 2020:674 https://doi.org/10.1186/s13662-020-03131-9 RESEARCH Open Access Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system Sukono 1* , Aceng Sambas 2 , Shaobo He 3 , Heng Liu 4 , Sundarapandian Vaidyanathan 5 , Yuyun Hidayat 1 and Jumadil Saputra 6 * Correspondence: sukono@unpad.ac.id 1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang, Indonesia Full list of author information is available at the end of the article Abstract In this paper, a fractional-order model of a financial risk dynamical system is proposed and the complex behavior of such a system is presented. The basic dynamical behavior of this financial risk dynamic system, such as chaotic attractor, Lyapunov exponents, and bifurcation analysis, is investigated. We find that numerical results display periodic behavior and chaotic behavior of the system. The results of theoretical models and numerical simulation are helpful for better understanding of other similar nonlinear financial risk dynamic systems. Furthermore, the adaptive fuzzy control for the fractional-order financial risk chaotic system is investigated on the fractional Lyapunov stability criterion. Finally, numerical simulation is given to confirm the effectiveness of the proposed method. Keywords: Chaos; Financial risk system; Fractional-order model; Dynamical analysis; Adaptive fuzzy control 1 Introduction Chaotic systems have received more attention due to their potential applications in eco- nomics and management, such as equity market indices: cases from the United Kingdom [1], monetary aggregates [2], business cycle [3], firm growth and R&D investment [4], chaotic behavior in foreign direct investment, and foreign capital investments [5, 6]. Some nonlinear models have been established to investigate the complex economic dy- namics such as Goodwin’s accelerate model [7], Van der Pol’s models [8], Duffing–Holmes model [9], Kaldoria model [10], and IS-LM model [11]. In recent years, chaotic economics has obtained intensive attention and has been raised to engineering applications for un- derstanding the complex behavior of the real financial market. In [12], Chen studied the chaos behavior in a financial system with the help of fractional order. In [13], Gao and Ma introduced a new finance chaotic system and exhibited Hopf bifurcation in the qualitative analysis of the finance system. In [14], Wang et al. described a finance chaotic system with delayed fractional order. In [15], Yu et al. used speed feedback control and linear feedback control for stabilizing hyperchaotic finance system to unstable equilibrium. In [16], Wang © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.