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<p>This paper introduces a novel class of functions within measure theory, namely measure pseudo <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-asymptotically affine periodic functions. This work naturally generalizes affine periodic functions and their various extensions. As application, we establish sufficient criteria for the existence and uniqueness of measure pseudo <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-asymptotically affine periodic solution to fractional differential equations, semilinear evolution equations and partial neutral functional differential equations with finite delay. The tools derived from semigroup theory and fixed point theorems. Finally, some interesting examples are presented to illustrate the main findings.</p>

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Measure Pseudo \(\mathcal {S}\)-Asymptotic Affine Periodicity on Banach Space and Applications

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Zhinan Xia,
  • Chao Xia,
  • Jinliang Chai

摘要

This paper introduces a novel class of functions within measure theory, namely measure pseudo \(\mathcal {S}\) S -asymptotically affine periodic functions. This work naturally generalizes affine periodic functions and their various extensions. As application, we establish sufficient criteria for the existence and uniqueness of measure pseudo \(\mathcal {S}\) S -asymptotically affine periodic solution to fractional differential equations, semilinear evolution equations and partial neutral functional differential equations with finite delay. The tools derived from semigroup theory and fixed point theorems. Finally, some interesting examples are presented to illustrate the main findings.