Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
Hong Li, Badreddine Meftah, Wedad Saleh, Hongyan Xu, Adem Kılıçman, Abdelghani Lakhdari
Abstract
This paper introduces new versions of Hermite–Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. This paper validates the derived inequalities through a numerical example with graphical representations and provides some practical applications, highlighting their relevance to special means. This study presents novel results, offering new insights into classical integrals as the fractional order β approaches 1, in addition to the fractional integrals we examined.
Topics & Concepts
MathematicsDifferentiable functionMidpointHadamard transformHermite polynomialsType (biology)Convex functionExponential functionPure mathematicsApplied mathematicsFractional calculusAlgebra over a fieldRegular polygonMathematical analysisGeometryBiologyEcologyMathematical Inequalities and ApplicationsMathematical functions and polynomialsFractional Differential Equations Solutions