Existence and Ulam–Hyers stability results for nonlinear fractional Langevin equation with modified argument


DEVELİ F.

Mathematical Methods in the Applied Sciences, vol.45, no.7, pp.3417-3425, 2022 (Journal Indexed in SCI Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.1002/mma.7987
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3417-3425
  • Keywords: Caputo fractional derivative, existence and uniqueness, fixed point, Langevin equation, Ulam-Hyers stability, INTEGRAL-EQUATIONS, UNIQUENESS, ORDERS

Abstract

© 2021 John Wiley & Sons, Ltd.In this paper, we give the existence and uniqueness result for the fractional order Langevin equation with modified argument by using the Bielecki norm. After, we consider a special form of this equation (delayed form) and then apply Burton's method to this special form to prove that there is a unique solution under weaker conditions than the other result. Further, we derive the Ulam–Hyers stability for this equation. Finally, two examples are given to illustrate our main results.