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 |
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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| _version_ | 1871646539828428800 |
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| author | Benhadda, Walid Mfadel, Ali El Kassidi, Abderrazak Elomari, M'hamed Benhadda, Walid Mfadel, Ali El Kassidi, Abderrazak Elomari, M'hamed |
| author_facet | Benhadda, Walid Mfadel, Ali El Kassidi, Abderrazak Elomari, M'hamed Benhadda, Walid Mfadel, Ali El Kassidi, Abderrazak Elomari, M'hamed |
| author_institution_txt_mv | [
{
"author": "Walid Benhadda",
"institution": "Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco"
},
{
"author": "Ali El Mfadel",
"institution": "Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco; Superior School of Technology, Sultan Moulay Slimane University, Khenifra, Morocco"
},
{
"author": "Abderrazak Kassidi",
"institution": "Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco"
},
{
"author": "M'hamed Elomari",
"institution": "Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco"
}
] |
| author_sort | Benhadda, Walid |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-07-24T15:24:12Z |
| description | 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_str_mv | 10.3842/umzh.v78i7-8.9432 |
| first_indexed | 2026-07-25T01:00:34Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9432 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-25T01:00:34Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-94322026-07-24T15:24:12Z Existence results for $\varphi$-Caputo fractional semilinear evolution equations Existence results for $\varphi$-Caputo fractional semilinear evolution equations Benhadda, Walid Mfadel, Ali El Kassidi, Abderrazak Elomari, M'hamed Benhadda, Walid Mfadel, Ali El Kassidi, Abderrazak Elomari, M'hamed C0-semigroup nonlocal condition φ-Caputo fractional derivative Measure of noncompactness $C_0$-semigroup nonlocal condition $\varphi$-Caputo fractional derivative Measure of noncompactness 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. УДК 517.937, 517.98, 517.23 Результати щодо існування розв'язків дробових напівлінійних еволюційних рівнянь із $\varphi$-похідною Капуто Досліджено існування м'яких розв'язків для нового класу нелокальних дробових напівлінійних інтегро-диференці\-альних еволюційних рівнянь з усюди нещільно визначеним замкненим лінійним оператором, що містить узагальнену дробову похідну Капуто \(\varphi\)-типу. Із застосуванням двох теорем про нерухому точку для ущільнювальних операторів у поєднанні з теорією \(C_0\)-напівгруп і поняттям міри некомпактності отримано достатні умови існування розв'язків. Наведено ілюстративний приклад, який демонструє застосовність і стійкість отриманих теоретичних результатів. Institute of Mathematics, NAS of Ukraine 2026-07-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9432 10.3842/umzh.v78i7-8.9432 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 7-8 (2026); 595–596 Український математичний журнал; Том 78 № 7-8 (2026); 595–596 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9432/10681 Copyright (c) 2026 Walid Benhadda, Ali El Mfadel, Abderrazak Kassidi, M'hamed Elomari |
| spellingShingle | Benhadda, Walid Mfadel, Ali El Kassidi, Abderrazak Elomari, M'hamed Benhadda, Walid Mfadel, Ali El Kassidi, Abderrazak Elomari, M'hamed Existence results for $\varphi$-Caputo fractional semilinear evolution equations |
| title | Existence results for $\varphi$-Caputo fractional semilinear evolution equations |
| title_alt | Existence results for $\varphi$-Caputo fractional semilinear evolution equations |
| title_full | Existence results for $\varphi$-Caputo fractional semilinear evolution equations |
| title_fullStr | Existence results for $\varphi$-Caputo fractional semilinear evolution equations |
| title_full_unstemmed | Existence results for $\varphi$-Caputo fractional semilinear evolution equations |
| title_short | Existence results for $\varphi$-Caputo fractional semilinear evolution equations |
| title_sort | existence results for $\varphi$-caputo fractional semilinear evolution equations |
| topic_facet | C0-semigroup nonlocal condition φ-Caputo fractional derivative Measure of noncompactness $C_0$-semigroup nonlocal condition $\varphi$-Caputo fractional derivative Measure of noncompactness |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9432 |
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