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<p>This paper investigates the stability of Caputo fractional-order discrete system with L1 operator, which was first proposed as a discrete scheme to discretize Caputo fractional-order continuous systems. In order to enlarge the applicability of fractional-order discrete theories and explore the preservation of the properties of discrete systems to continuous systems, the L1 operator is considered in this paper as a discrete operator. Then the basic properties of L1 operator are investigated, including semigroup properties and so on. Meanwhile, the existence and uniqueness of the global solution for nonautonomous systems with L1 operator are investigated. Furthermore, fractional-order Lyapunov methods are used to establish the global stability conditions of autonomous and nonautonomous systems with L1 operator, respectively. Finally, two examples are provided to demonstrate the main theoretical results.</p>

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Stability analysis for Caputo fractional-order discrete system with first-order operator

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Zhenzhen Lu,
  • Xiangyun Meng,
  • YangQuan Chen,
  • Ahmed Rahmani,
  • Guojian Ren,
  • Yongguang Yu

摘要

This paper investigates the stability of Caputo fractional-order discrete system with L1 operator, which was first proposed as a discrete scheme to discretize Caputo fractional-order continuous systems. In order to enlarge the applicability of fractional-order discrete theories and explore the preservation of the properties of discrete systems to continuous systems, the L1 operator is considered in this paper as a discrete operator. Then the basic properties of L1 operator are investigated, including semigroup properties and so on. Meanwhile, the existence and uniqueness of the global solution for nonautonomous systems with L1 operator are investigated. Furthermore, fractional-order Lyapunov methods are used to establish the global stability conditions of autonomous and nonautonomous systems with L1 operator, respectively. Finally, two examples are provided to demonstrate the main theoretical results.