Existence and stability analysis of solution for fractional delay differential equations

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DEVELİ F., DUMAN O.

Filomat, vol.37, no.6, pp.1869-1878, 2023 (SCI-Expanded) identifier

  • 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
  • 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.