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<p>In this paper, we investigate the existence of mild solution for stochastic delay differential equations involving a non-dense domain, utilizing the Hilfer fractional derivative, which generalizes the well-known Riemann-Liouville fractional derivative. The existence results are derived using semigroup theory, fractional calculus, Wiener process, and the fixed point methods. Fixed point techniques, particularly those based on Sadovskii’s fixed point theorem, play a significant role in establishing the main results. Additionally, an illustrative example is provided to demonstrate the applicability of the theoretical findings.</p>

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An analysis on the existence results for Hilfer fractional stochastic differential equations with finite delay and non-dense domain

  • 期刊论文

  • 发表日期：

    2025年6月10日

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  • A. Priyadharshini,
  • V. Vijayakumar

摘要

In this paper, we investigate the existence of mild solution for stochastic delay differential equations involving a non-dense domain, utilizing the Hilfer fractional derivative, which generalizes the well-known Riemann-Liouville fractional derivative. The existence results are derived using semigroup theory, fractional calculus, Wiener process, and the fixed point methods. Fixed point techniques, particularly those based on Sadovskii’s fixed point theorem, play a significant role in establishing the main results. Additionally, an illustrative example is provided to demonstrate the applicability of the theoretical findings.