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

DEVELİ F.

Mathematical Methods in the Applied Sciences, cilt.45, sa.7, ss.3417-3425, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 7
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1002/mma.7987
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.3417-3425
  • Anahtar Kelimeler: Caputo fractional derivative, existence and uniqueness, fixed point, Langevin equation, Ulam-Hyers stability, INTEGRAL-EQUATIONS, UNIQUENESS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

© 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.