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<p>We study the existence of resolving families of operators for equations with the Riemann– Liouville derivatives. We find Hille–Yosida type conditions on the operator that are necessary and sufficient existence conditions and obtain Phillips approximations of operators of these families. Examples of unbounded operators generating resolving families are given.</p>

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Strongly Continuous Resolving Families of Equations with Riemann–Liouville Derivative

  • 期刊论文

  • 发表日期：

    2025年1月11日

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  • Vladimir E. Fedorov,
  • Dar’ya A. Vershinina

摘要

We study the existence of resolving families of operators for equations with the Riemann– Liouville derivatives. We find Hille–Yosida type conditions on the operator that are necessary and sufficient existence conditions and obtain Phillips approximations of operators of these families. Examples of unbounded operators generating resolving families are given.