Bounds for the Error in Approximating a Fractional Integral by Simpson's Rule

Budak H., Hezenci F., Kara H., Sarikaya M. Z.

MATHEMATICS, cilt.11, sa.10, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 10
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/math11102282
  • Dergi Adı: MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

Simpson's rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann-Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson's inequalities is the first paper in the literature as a method.