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<p>This paper develops a comprehensive analytical framework for the stability analysis of higher-order discrete fractional systems governed by the Atangana-Baleanu-Riemann-Liouville difference operator with fractional order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\omega \in (1,2]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ω</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>. In contrast to existing studies primarily focused on lower-order systems, this work explores the complex dynamical behavior arising from higher-order fractional effects, such as inertial and oscillatory memory responses. The existence and uniqueness of solutions are established using the Banach fixed-point theorem, and new sufficient conditions for Ulam-Hyers and Ulam-Hyers-Rassias stability are derived. Numerical simulations are provided to illustrate and validate the theoretical results, confirming the effectiveness and practical relevance of the proposed framework.</p>

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Ulam-Hyers Stability Results for Atangana-Baleanu Discrete Fractional Systems of Order \(\omega \in (1,2]\)

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Anshul Sharma,
  • Mohit Kumar,
  • S. N. Mishra,
  • Anurag Shukla

摘要

This paper develops a comprehensive analytical framework for the stability analysis of higher-order discrete fractional systems governed by the Atangana-Baleanu-Riemann-Liouville difference operator with fractional order \(\omega \in (1,2]\) ω ∈ ( 1 , 2 ] . In contrast to existing studies primarily focused on lower-order systems, this work explores the complex dynamical behavior arising from higher-order fractional effects, such as inertial and oscillatory memory responses. The existence and uniqueness of solutions are established using the Banach fixed-point theorem, and new sufficient conditions for Ulam-Hyers and Ulam-Hyers-Rassias stability are derived. Numerical simulations are provided to illustrate and validate the theoretical results, confirming the effectiveness and practical relevance of the proposed framework.