一些新的分数阶积分不等式的分析与应用

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-10-31 DOI:10.3390/fractalfract7110797

Sofia Ramzan, Muhammad Uzair Awan, Silvestru Sever Dragomir, Bandar Bin-Mohsin, Muhammad Aslam Noor

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引用次数: 0

摘要

提出了一种新的参数化分数阶积分恒等式。利用这一辅助结果和映射的s-凸性，导出了一系列经典不等式的分数型，包括辛普森不等式、中点不等式和梯形不等式。此外，还探讨了我们的主要结果在实数的特殊均值中的一些应用。此外，我们还推导出一种新的求解非线性方程的通用数值格式，展示了我们的主要结果在数值分析中的应用。

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Analysis and Applications of Some New Fractional Integral Inequalities

This paper presents a novel parameterized fractional integral identity. By using this auxiliary result and the s-convexity property of the mapping, a series of fractional variants of certain classical inequalities, including Simpson’s, midpoint, and trapezoidal-type inequalities, have been derived. Additionally, some applications of our main outcomes to special means of real numbers have been explored. Moreover, we have derived a new generic numerical scheme for solving non-linear equations, demonstrating an application of our main results in numerical analysis.

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.