Existence theory for $\psi$-Caputo fractional differential equations
UDC 517.9 The target of this paper is to handle a nonlocal boundary-value problem for a specific kind of nonlinear fractional differential equations encapsuling a collective fractional derivative known as the $\psi$-Caputo fractional operator. The applied fractional operator generated b...
Saved in:
| Date: | 2025 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7669 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512697265684480 |
|---|---|
| author | Bendrici, Nadhir Boutiara, Abdellatif Boumedien-Zidani, Malika Bendrici, Nadhir Boutiara, Abdellatif Boumedien-Zidani, Malika |
| author_facet | Bendrici, Nadhir Boutiara, Abdellatif Boumedien-Zidani, Malika Bendrici, Nadhir Boutiara, Abdellatif Boumedien-Zidani, Malika |
| author_sort | Bendrici, Nadhir |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-04-16T12:01:18Z |
| description | UDC 517.9
The target of this paper is to handle a nonlocal boundary-value problem for a specific kind of nonlinear fractional differential equations encapsuling a collective fractional derivative known as the $\psi$-Caputo fractional operator. The applied fractional operator generated by the kernel is of the following kind: $k(t,s)=\psi (t)-\psi(s).$  The existence of the solutions of the above-mentioned equations is tackled by using Mönch's fixed-point theorem combined with the technique of measures of noncompactness. In addition, we discuss the problem of stability within the scope of the Ulam–Hyers stability criteria for the main fractional system.  Finally, an example is given to illustrate the viability of the reported results. |
| doi_str_mv | 10.3842/umzh.v76i9.7669 |
| first_indexed | 2026-03-24T03:32:54Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7669 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:54Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-76692025-04-16T12:01:18Z Existence theory for $\psi$-Caputo fractional differential equations Existence theory for $\psi$-Caputo fractional differential equations Bendrici, Nadhir Boutiara, Abdellatif Boumedien-Zidani, Malika Bendrici, Nadhir Boutiara, Abdellatif Boumedien-Zidani, Malika -caputo - Fractional derivatives equations - Boundary value problem - M¨onch fixed point theorem, Measure of noncompactness $\psi$-Caputo fractional differential equations Boundary value problem Monch fixed point theorem Measure of non-compacteness UDC 517.9 The target of this paper is to handle a nonlocal boundary-value problem for a specific kind of nonlinear fractional differential equations encapsuling a collective fractional derivative known as the $\psi$-Caputo fractional operator. The applied fractional operator generated by the kernel is of the following kind: $k(t,s)=\psi (t)-\psi(s).$  The existence of the solutions of the above-mentioned equations is tackled by using Mönch's fixed-point theorem combined with the technique of measures of noncompactness. In addition, we discuss the problem of stability within the scope of the Ulam–Hyers stability criteria for the main fractional system.  Finally, an example is given to illustrate the viability of the reported results. УДК 517.9 Теорія існування для дробово-раціональних $\psi$-Капуто рівнянь Метою цієї роботи є розв'язання нелокальної крайової задачі для певного типу нелінійних диференціальних рівнянь з частинними похідними, що містять колективну дробову похідну, відому як дробовий оператор $\psi$-Капуто. Дробовий оператор, що використовується, згенеровано ядром. Він має вигляд $k(t,s)=\psi (t)-\psi(s).$  Існування розв'язків вищезгаданих рівнянь досліджується за допомогою теореми Монча про фіксовану точку в поєднанні з технікою мір некомпактності. Крім того, обговорено проблему стійкості для основної системи дробових рівнянь в рамках критеріїв стійкості Улама–Хаєрса.  Насамкінець наведено приклад, який ілюструє життєздатність отриманих результатів. Institute of Mathematics, NAS of Ukraine 2025-04-16 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7669 10.3842/umzh.v76i9.7669 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 9 (2024); 1291 - 1303 Український математичний журнал; Том 76 № 9 (2024); 1291 - 1303 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7669/10163 Copyright (c) 2024 Abdellatif boutiara |
| spellingShingle | Bendrici, Nadhir Boutiara, Abdellatif Boumedien-Zidani, Malika Bendrici, Nadhir Boutiara, Abdellatif Boumedien-Zidani, Malika Existence theory for $\psi$-Caputo fractional differential equations |
| title | Existence theory for $\psi$-Caputo fractional differential equations |
| title_alt | Existence theory for $\psi$-Caputo fractional differential equations |
| title_full | Existence theory for $\psi$-Caputo fractional differential equations |
| title_fullStr | Existence theory for $\psi$-Caputo fractional differential equations |
| title_full_unstemmed | Existence theory for $\psi$-Caputo fractional differential equations |
| title_short | Existence theory for $\psi$-Caputo fractional differential equations |
| title_sort | existence theory for $\psi$-caputo fractional differential equations |
| topic_facet | -caputo - Fractional derivatives equations - Boundary value problem - M¨onch fixed point theorem Measure of noncompactness $\psi$-Caputo fractional differential equations Boundary value problem Monch fixed point theorem Measure of non-compacteness |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7669 |
| work_keys_str_mv | AT bendricinadhir existencetheoryforpsicaputofractionaldifferentialequations AT boutiaraabdellatif existencetheoryforpsicaputofractionaldifferentialequations AT boumedienzidanimalika existencetheoryforpsicaputofractionaldifferentialequations AT bendricinadhir existencetheoryforpsicaputofractionaldifferentialequations AT boutiaraabdellatif existencetheoryforpsicaputofractionaldifferentialequations AT boumedienzidanimalika existencetheoryforpsicaputofractionaldifferentialequations |