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<p>In this paper, we focus on a class of uncertain differential equations driven by fractional Liu process, which is the twin of fractional Brownian motion in the structure of uncertain theory. By the Carathéodory approximation, we prove the existence and uniqueness of solutions for the considered equations under some non-Lipschitz conditions. Subsequently, we consider the stability properties with respect to initial data and coefficients by establishing some Bihari type fractional inequalities, generalizing some known results. Finally, an example is provided to illustrate the effectiveness of our main results.</p>

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Uncertain differential equations driven by fractional Liu process

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Zhi Li,
  • Liping Xu

摘要

In this paper, we focus on a class of uncertain differential equations driven by fractional Liu process, which is the twin of fractional Brownian motion in the structure of uncertain theory. By the Carathéodory approximation, we prove the existence and uniqueness of solutions for the considered equations under some non-Lipschitz conditions. Subsequently, we consider the stability properties with respect to initial data and coefficients by establishing some Bihari type fractional inequalities, generalizing some known results. Finally, an example is provided to illustrate the effectiveness of our main results.