On error bounds for Milne's formula in conformable fractional operators
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...
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Institute of Mathematics, NAS of Ukraine
2024
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512678971179008 |
|---|---|
| author | Hezenci, Fatih Budak, Hüseyin Hezenci, Fatih Budak, Hüseyin |
| author_facet | Hezenci, Fatih Budak, Hüseyin Hezenci, Fatih Budak, Hüseyin |
| author_sort | Hezenci, Fatih |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-08-10T06:39:13Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v76i7.7513 |
| first_indexed | 2026-03-24T03:32:37Z |
| format | Article |
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| id | umjimathkievua-article-7513 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:37Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-75132024-08-10T06:39:13Z On error bounds for Milne's formula in conformable fractional operators On error bounds for Milne's formula in conformable fractional operators Hezenci, Fatih Budak, Hüseyin Hezenci, Fatih Budak, Hüseyin quadrature formulae fractional conformable integrals open Newton-Cotes formulas Milne's formula 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. УДК 517.9 Про межі похибки формули Мілна для конформних дробових операторів Формула Мілна – це математичний вираз, який використовується для наближеного обчислення значення означеного інтеграла. Ця формула особливо корисна для задач, що зустрічаються у фізиці, техніці та інших наукових дисцип\-лінах. У цій статті доведено рівність для  конформних дробових інтегралів. За допомогою цієї рівності отримано оцінку похибки однієї з відкритих формул Ньютона–Котеса, а саме формули Мілна, для випадку диференційовних опуклих функцій в рамках дробового та класичного числення. Навіть більше, ми наводимо наші результати, використовуючи окремі випадки отриманих теорем. Institute of Mathematics, NAS of Ukraine 2024-08-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7513 10.3842/umzh.v76i7.7513 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 7 (2024); 1069 - 1085 Український математичний журнал; Том 76 № 7 (2024); 1069 - 1085 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7513/10061 Copyright (c) 2024 fatih HEZENCİ; Huseyin Budak |
| spellingShingle | Hezenci, Fatih Budak, Hüseyin Hezenci, Fatih Budak, Hüseyin On error bounds for Milne's formula in conformable fractional operators |
| title | On error bounds for Milne's formula in conformable fractional operators |
| title_alt | On error bounds for Milne's formula in conformable fractional operators |
| title_full | On error bounds for Milne's formula in conformable fractional operators |
| title_fullStr | On error bounds for Milne's formula in conformable fractional operators |
| title_full_unstemmed | On error bounds for Milne's formula in conformable fractional operators |
| title_short | On error bounds for Milne's formula in conformable fractional operators |
| title_sort | on error bounds for milne's formula in conformable fractional operators |
| topic_facet | quadrature formulae fractional conformable integrals open Newton-Cotes formulas Milne's formula |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7513 |
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