Existence results for $\varphi$-Caputo fractional semilinear evolution equations

UDC 517.937, 517.98, 517.23 We study the existence of mild solutions for a new class of nonlocal fractional semilinear integrodifferential evolution equations with a nondensely defined closed linear operator involving the generalized \( \varphi \)-Caputo fractional derivative.  By applying two fixed...

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Bibliographic Details
Date:2026
Main Authors: Benhadda, Walid, Mfadel, Ali El, Kassidi, Abderrazak, Elomari, M'hamed
Format: Article
Language:English
Published: Institute of Mathematics, NAS of Ukraine 2026
Online Access:https://umj.imath.kiev.ua/index.php/umj/article/view/9432
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Journal Title:Ukrains’kyi Matematychnyi Zhurnal

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Ukrains’kyi Matematychnyi Zhurnal
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Summary:UDC 517.937, 517.98, 517.23 We study the existence of mild solutions for a new class of nonlocal fractional semilinear integrodifferential evolution equations with a nondensely defined closed linear operator involving the generalized \( \varphi \)-Caputo fractional derivative.  By applying two fixed-point theorems for condensing operators, in combination with the \( C_0 \)-semigroup theory and the concept of noncompactness measure, we derive sufficient conditions for the existence of solutions. An illustrative example is presented to highlight the applicability and robustness of our theoretical findings.
DOI:10.3842/umzh.v78i7-8.9432