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Weddle's inequalities in fractional space

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Název: Weddle's inequalities in fractional space
Autoři: Qi Liu, Muhammad Zakria Javed, Muhammad Uzair Awan, Yuanheng Wang, Ahmed M. Zidan
Zdroj: Ain Shams Engineering Journal, Vol 16, Iss 10, Pp 103550- (2025)
Informace o vydavateli: Elsevier, 2025.
Rok vydání: 2025
Sbírka: LCC:Engineering (General). Civil engineering (General)
Témata: Fractional Weddle's inequality, Convex function, Hölder's inequality, Applications, Non-linear analysis, Engineering (General). Civil engineering (General), TA1-2040
Popis: The literature clearly demonstrates the investigation of various approaches, including Newton–Cotes procedures, to approximate the integrals with high accuracy. A closed method based on seven points that approximates the quantities by a sixth-degree polynomial is known as Weddle's rule. This study assesses the error analysis of this renowned procedure to seek out the shortcomings of classic error inequality to produce new bounds for a larger space of functions within the fractional calculus. A new Riemann-Liouville fractional identity for differentiable functions is developed. To construct various estimates of Weddle's inequality, we utilize this identity together with properties of several benchmark functions like convex, Lipschitz, and bounded variation functions. Graphical and numerical comparisons are supplied to justify the obtained results. Lastly, we present the applicable analysis of primary findings to the theory of means, composite error bounds, and particularly a bi-quadratic iterative method is developed.
Druh dokumentu: article
Popis souboru: electronic resource
Jazyk: English
ISSN: 2090-4479
Relation: http://www.sciencedirect.com/science/article/pii/S2090447925002916; https://doaj.org/toc/2090-4479
DOI: 10.1016/j.asej.2025.103550
Přístupová URL adresa: https://doaj.org/article/3de9b394db6d45aca90b2d72e95f3752
Přístupové číslo: edsdoj.3de9b394db6d45aca90b2d72e95f3752
Databáze: Directory of Open Access Journals
Popis
Abstrakt:The literature clearly demonstrates the investigation of various approaches, including Newton–Cotes procedures, to approximate the integrals with high accuracy. A closed method based on seven points that approximates the quantities by a sixth-degree polynomial is known as Weddle's rule. This study assesses the error analysis of this renowned procedure to seek out the shortcomings of classic error inequality to produce new bounds for a larger space of functions within the fractional calculus. A new Riemann-Liouville fractional identity for differentiable functions is developed. To construct various estimates of Weddle's inequality, we utilize this identity together with properties of several benchmark functions like convex, Lipschitz, and bounded variation functions. Graphical and numerical comparisons are supplied to justify the obtained results. Lastly, we present the applicable analysis of primary findings to the theory of means, composite error bounds, and particularly a bi-quadratic iterative method is developed.
ISSN:20904479
DOI:10.1016/j.asej.2025.103550