Existence theory for $\psi$-Caputo fractional differential equations

Nadhir Bendrici; Abdellatif Boutiara; Malika Boumedien-Zidani

doi:10.3842/umzh.v76i9.7669

Nadhir Bendrici Laboratory of Dynamic Systems, University of Science and Technology Houari Boumediene, Bab ezzouar, Algeria
Abdellatif Boutiara Department of Mathematics and Computer Science, University of Ghardaia, Algeria
Malika Boumedien-Zidani Laboratory of Dynamic Systems, University of Science and Technology Houari Boumediene, Bab ezzouar, Algeria

DOI: https://doi.org/10.3842/umzh.v76i9.7669

Анотація

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.

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