Existence and stability analysis of solution for fractional delay differential equations
Filomat, vol.37, no.6, pp.1869-1878, 2023 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 37 Issue: 6
- Publication Date: 2023
- Doi Number: 10.2298/fil2306869d
- Journal Name: Filomat
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
- Page Numbers: pp.1869-1878
- Keywords: Delay differential equation, Existence and uniqueness, Fractional-order, Hyers-Ulam stability
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
Abstract
© 2023, University of Nis. All rights reserved.In this article, we give some results for fractional-order delay differential equations. In the first result, we prove the existence and uniqueness of solution by using Bielecki norm effectively. In the second result, we consider a constant delay form of this problem. Then we apply Burton’s method to this special form to prove that there is only one solution. Finally, we prove a result regarding the Hyers-Ulam stability of this problem. Moreover, in these results, we omit the conditions for contraction constants seen in many papers.