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<p>In this paper, within the framework of (<i>p</i>,&#xa0;<i>q</i>)-integrals, we first obtain an estimate for increasing functions different from that in classical integrals and establish a new Gronwall inequality. Subsequently, we present the expression for the solution to the first-order linear (<i>p</i>,&#xa0;<i>q</i>)-difference equation and prove the existence and uniqueness of the solution to the first-order nonlinear (<i>p</i>,&#xa0;<i>q</i>)-difference equation. Furthermore, by employing the newly established Gronwall inequality, we study the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of the first-order (<i>p</i>,&#xa0;<i>q</i>)-difference equations. Finally, several illustrative examples are provided to verify the validity of the theoretical results.</p>

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Existence, uniqueness and Ulam stability of the first-order (p, q)-difference equations

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Jietian Dong,
  • JinRong Wang

摘要

In this paper, within the framework of (p, q)-integrals, we first obtain an estimate for increasing functions different from that in classical integrals and establish a new Gronwall inequality. Subsequently, we present the expression for the solution to the first-order linear (p, q)-difference equation and prove the existence and uniqueness of the solution to the first-order nonlinear (p, q)-difference equation. Furthermore, by employing the newly established Gronwall inequality, we study the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of the first-order (p, q)-difference equations. Finally, several illustrative examples are provided to verify the validity of the theoretical results.