Existence and stability results for nonlocal boundary value problems of fractional order

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Ertürk V. S., Ali A., Shah K., Kumar P., Abdeljawad T.

BOUNDARY VALUE PROBLEMS, cilt.2022, sa.1, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2022 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1186/s13661-022-01606-0
  • Dergi Adı: BOUNDARY VALUE PROBLEMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: CFD, BVP, Existence and uniqueness, g-H-U stability, HYERS-ULAM STABILITY, LINEAR-DIFFERENTIAL EQUATIONS
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In this paper, we prove the existence and uniqueness of solutions for the nonlocal boundary value problem (BVP) using Caputo fractional derivative (CFD). We derive Green's function and give some estimation for it to derive our main results. The main principles applied to investigate our results are based on the Banach contraction fixed point theorem and Schauder fixed point approach. We dwell in detail on some results concerning the Hyers-Ulam (H-U) type and generalized H-U (g-H-U) type stability also for problem we are considering. We justify our results with an illustrative example.