Analysis and Applications of Some New Fractional Integral Inequalities

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.

Keywords

• ?-convex mappings
• 1 3 formula%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> Simpson’s <named-content content-type="inline-formula/inline/equation"><inline-formula> <mml:math id="mm90002"> <mml:semantics> <mml:mrow> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>3</mml:mn> </mml:mfrac> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> formula
• midpoint formula
• trapezoidal formula
• integral inequalities
• fractional calculus