On Error Bounds for Milne's Formula in Conformable Fractional Operators

Hezenci F., Budak H.

UKRAINIAN MATHEMATICAL JOURNAL, cilt.76, sa.7, ss.1214-1232, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 76 Sayı: 7
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s11253-024-02382-z
  • Dergi Adı: UKRAINIAN MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1214-1232
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

Milne's formula is a mathematical expression used to approximate the value of a definite integral. This formula is especially useful for problems encountered in physics, engineering, and various other scientific disciplines. We establish an equality for conformable fractional integrals. With the help of this equality, we obtain error bounds for one of the open Newton-Cotes formulas, namely, Milne's formula for the case of differentiable convex functions within the framework of fractional and classical calculus. Furthermore, we provide our results by using special cases of the obtained theorems.