Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems
Arab Journal of Basic and Applied Sciences, vol.31, no.1, pp.225-241, 2024 (Scopus)
- Publication Type: Article / Article
- Volume: 31 Issue: 1
- Publication Date: 2024
- Doi Number: 10.1080/25765299.2024.2334130
- Journal Name: Arab Journal of Basic and Applied Sciences
- Journal Indexes: Scopus
- Page Numbers: pp.225-241
- Keywords: 26A33, 34A12, 34G20, Banach spaces, coupled systems, existence, generalized Gronwall inequality, generalized Hilfer fractional derivative, measure of noncompactness, Mittag-Leffler function, Ulam-Hyers stability
- Ankara Yıldırım Beyazıt University Affiliated: Yes
Abstract
In this paper, we delve into the analysis of the existence and stability concerning the (Formula presented.) -Mittag-Leffler-Ulam-Hyers within a particular class of coupled systems related to boundary value problems. These problems entail implicit nonlinear fractional differential equations and (Formula presented.) -generalized ϑ-Hilfer fractional derivatives. To achieve our objectives, we employ the Mönch fixed point theorem, complemented by the application of the measure of noncompactness technique and an extension of the well-established Gronwall inequality. Furthermore, we include an illustrative example to showcase the practical utility of our results. The significance of our research lies in examining a comprehensive problem involving coupled systems, which serves as a generalization encompassing all the works mentioned in the introduction. It is viewed as a logical extension and continuation within the framework of this continually evolving theory.