Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals
Abstract Milne’s inequality provides an upper bound for the error in definite integral approximations using Milne’s rule, making it a useful tool for evaluating the rule’s precision. For this reason, this inequality is widely applied in engineering, physics, and applied mathematics. Additionally, co...
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2025-05-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02049-z |
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| author | Esra Üneş İzzettin Demir |
| author_facet | Esra Üneş İzzettin Demir |
| author_sort | Esra Üneş |
| collection | DOAJ |
| description | Abstract Milne’s inequality provides an upper bound for the error in definite integral approximations using Milne’s rule, making it a useful tool for evaluating the rule’s precision. For this reason, this inequality is widely applied in engineering, physics, and applied mathematics. Additionally, conformable fractional integral operators establish a stronger relationship between classical and fractional calculus, enhancing the modeling, analysis, and resolution of complex problems. Therefore, we focus on the study of conformable fractional integral operators and Milne-type inequalities, which have significant applications in various fields. In this study, we first obtain an integral identity involving conformable fractional integral operators and twice-differentiable functions. Building on this new identity, we develop various perturbed Milne-type integral inequalities for twice-differentiable convex functions. We also validate them numerically through examples, computational analysis, and visual representations. In conclusion, it is evident that our findings significantly enhance and expand upon prior findings regarding integral inequalities. In addition to improving the scope of previous discoveries, the obtained results offer meaningful approaches and methods for tackling mathematical and scientific issues. |
| format | Article |
| id | doaj-art-ea0cd24b049f4ecf8247f5c33a1f555e |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-ea0cd24b049f4ecf8247f5c33a1f555e2025-08-20T03:48:18ZengSpringerOpenBoundary Value Problems1687-27702025-05-012025112910.1186/s13661-025-02049-zError estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integralsEsra Üneş0İzzettin DemirDepartment of Mathematics, Faculty of Science and Arts, Duzce UniversityAbstract Milne’s inequality provides an upper bound for the error in definite integral approximations using Milne’s rule, making it a useful tool for evaluating the rule’s precision. For this reason, this inequality is widely applied in engineering, physics, and applied mathematics. Additionally, conformable fractional integral operators establish a stronger relationship between classical and fractional calculus, enhancing the modeling, analysis, and resolution of complex problems. Therefore, we focus on the study of conformable fractional integral operators and Milne-type inequalities, which have significant applications in various fields. In this study, we first obtain an integral identity involving conformable fractional integral operators and twice-differentiable functions. Building on this new identity, we develop various perturbed Milne-type integral inequalities for twice-differentiable convex functions. We also validate them numerically through examples, computational analysis, and visual representations. In conclusion, it is evident that our findings significantly enhance and expand upon prior findings regarding integral inequalities. In addition to improving the scope of previous discoveries, the obtained results offer meaningful approaches and methods for tackling mathematical and scientific issues.https://doi.org/10.1186/s13661-025-02049-zMilne-type integral inequalitiesConvex functionsRiemann–Liouville fractional integralsConformable fractional integrals |
| spellingShingle | Esra Üneş İzzettin Demir Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals Boundary Value Problems Milne-type integral inequalities Convex functions Riemann–Liouville fractional integrals Conformable fractional integrals |
| title | Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals |
| title_full | Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals |
| title_fullStr | Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals |
| title_full_unstemmed | Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals |
| title_short | Error estimates for perturbed Milne-type inequalities by twice-differentiable functions using conformable fractional integrals |
| title_sort | error estimates for perturbed milne type inequalities by twice differentiable functions using conformable fractional integrals |
| topic | Milne-type integral inequalities Convex functions Riemann–Liouville fractional integrals Conformable fractional integrals |
| url | https://doi.org/10.1186/s13661-025-02049-z |
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