Analysis and Applications of Some New Fractional Integral Inequalities

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Ramzan, Sofia ORCID: 0000-0002-0158-0671, Awan, Muhammad Uzair ORCID: 0000-0002-1019-9485, Dragomir, Sever S ORCID: 0000-0003-2902-6805, Bin-Mohsin, Bandar ORCID: 0000-0002-2160-4159 and Noor, Muhammad Aslam ORCID: 0000-0001-6105-2435 (2023) Analysis and Applications of Some New Fractional Integral Inequalities. Fractal and Fractional, 7 (11). ISSN 2504-3110

Abstract

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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Item type Article
URI https://vuir.vu.edu.au/id/eprint/47595
DOI 10.3390/fractalfract7110797
Official URL https://www.mdpi.com/2504-3110/7/11/797
Subjects Current > FOR (2020) Classification > 4901 Applied mathematics
Current > Division/Research > College of Science and Engineering
Keywords s-convex mappings; Simpson’s 1/3 formula; midpoint formula; trapezoidal formula; integral inequalities; fractional calculus; basins of attraction
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