Scholarlink

<p>This study investigates the existence and uniqueness of solutions to fractional stochastic differential equations incorporating G-Lévy jumps. The theoretical framework is established by employing the Mittag-Leffler function, a generalized form of Gronwall’s inequality and the Picard approximation technique. The boundedness of exact solutions and Picard approximate solutions has been derived. Error estimates between the approximate solutions and the actual solutions are established. Additionally, the continuous dependence of solutions on initial values is explored. The Hölder’s continuity of the solutions is rigorously established. To demonstrate the practical relevance of the theoretical findings, a detailed example is provided.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the existence and continuity of solutions to fractional stochastic differential equations in the framework of G-Lévy jumps

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月13日

查看全文
  • Rahman Ullah,
  • Muhammad Farooq,
  • Faiz Faizullah,
  • Maryam A. Alghafli,
  • Nabil Mlaiki

摘要

This study investigates the existence and uniqueness of solutions to fractional stochastic differential equations incorporating G-Lévy jumps. The theoretical framework is established by employing the Mittag-Leffler function, a generalized form of Gronwall’s inequality and the Picard approximation technique. The boundedness of exact solutions and Picard approximate solutions has been derived. Error estimates between the approximate solutions and the actual solutions are established. Additionally, the continuous dependence of solutions on initial values is explored. The Hölder’s continuity of the solutions is rigorously established. To demonstrate the practical relevance of the theoretical findings, a detailed example is provided.