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.

Automated summary

This paper presents a novel parameterized fractional integral identity and derives a series of fractional variants of certain classical inequalities by using this result and the convexity property of the mapping. It also explores applications of the main outcomes to special means of real numbers and proposes a new numerical scheme for solving non-linear equations, demonstrating its application in numerical analysis.