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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| Date: | 2026 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| 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| 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. |
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| DOI: | 10.3842/umzh.v78i7-8.9432 |