On Some Error Bounds for Milne’s Formula in Fractional Calculus

Muhammad Aamir Ali, Zhiyue Zhang () and Michal Fečkan ()
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Muhammad Aamir Ali: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Zhiyue Zhang: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Michal Fečkan: Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia

Mathematics, 2022, vol. 11, issue 1, 1-11

Abstract: In this paper, we found the error bounds for one of the open Newton–Cotes formulas, namely Milne’s formula for differentiable convex functions in the framework of fractional and classical calculus. We also give some mathematical examples to show that the newly established bounds are valid for Milne’s formula.

Keywords: open Newton–Cotes formulas; fractional calculus; convex functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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