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<p>This paper investigates the asymptotic behavior of fractional resolvent families in Banach spaces. We establish new results on operator equivalence under asymptotic approximation conditions, develop stability criteria for resolvent families, and extend Datko’s theorem to the fractional setting. The main technical tools include spectral theory, Laplace transform methods, and refined estimates of Mittag-Leffler functions.</p>

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Distance between two resolvent families

  • 期刊论文

  • 发表日期：

    2025年9月13日

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  • Chen-Yu Li

摘要

This paper investigates the asymptotic behavior of fractional resolvent families in Banach spaces. We establish new results on operator equivalence under asymptotic approximation conditions, develop stability criteria for resolvent families, and extend Datko’s theorem to the fractional setting. The main technical tools include spectral theory, Laplace transform methods, and refined estimates of Mittag-Leffler functions.