On error bounds for Milne's formula in conformable fractional operators

Fatih Hezenci; Hüseyin Budak

doi:10.3842/umzh.v76i7.7513

Fatih Hezenci Department of Mathematics, Faculty of Science and Arts, Duzce University, Turkey https://orcid.org/0000-0003-1008-5856
Hüseyin Budak Department of Mathematics, Faculty of Science and Arts, Duzce University, Turkey

DOI: https://doi.org/10.3842/umzh.v76i7.7513

Keywords: quadrature formulae, fractional conformable integrals, open Newton-Cotes formulas, Milne's formula

Abstract

UDC 517.9

Milne's formula is a mathematical expression used to approximate the value of a definite integral. The formula is particularly 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.

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