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<p>This paper investigates the existence of mild solutions for a class of semi-linear fractional evolution equations in Banach spaces under local conditions. The analysis relies on semigroup theory, the generalized <i>ψ</i>-Laplace transform, as well as the Schauder fixed point theorem. Our results extend previous works involving the classical Caputo fractional derivative. Furthermore, we establish the controllability of the proposed time-fractional system. To support our theoretical findings, we provide a concrete and non-trivial example.</p>

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Existence and controllability results for fractional evolution equations via β-order resolvent operators in Banach spaces

  • 期刊论文

  • 发表日期：

    2025年4月14日

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  • Ismail Sadouki,
  • Ali El Mfadel,
  • Abdelaziz Qaffou

摘要

This paper investigates the existence of mild solutions for a class of semi-linear fractional evolution equations in Banach spaces under local conditions. The analysis relies on semigroup theory, the generalized ψ-Laplace transform, as well as the Schauder fixed point theorem. Our results extend previous works involving the classical Caputo fractional derivative. Furthermore, we establish the controllability of the proposed time-fractional system. To support our theoretical findings, we provide a concrete and non-trivial example.