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, vol.2022, no.1, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2022 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1186/s13661-022-01606-0
  • Journal Name: BOUNDARY VALUE PROBLEMS
  • Journal Indexes: 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
  • Keywords: CFD, BVP, Existence and uniqueness, g-H-U stability, HYERS-ULAM STABILITY, LINEAR-DIFFERENTIAL EQUATIONS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

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.