Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities
Mustafa Gürbüz, Ahmet Ocak Akdemi̇r, Saima Rashid, Erhan Set
Abstract
Abstract In this article, firstly, Hermite–Hadamard’s inequality is generalized via a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. Then a new kernel is obtained and a new theorem valid for convex functions is proved for fractional order integrals. Also, some applications of our main findings are given.
Topics & Concepts
MathematicsHermite polynomialsFractional calculusHadamard transformConvex functionKernel (algebra)Type (biology)Operator (biology)Pure mathematicsInequalityOrder (exchange)Regular polygonMathematical analysisApplied mathematicsBiologyFinanceBiochemistryEcologyGeometryChemistryTranscription factorGeneRepressorEconomicsMathematical Inequalities and ApplicationsFractional Differential Equations SolutionsNonlinear Differential Equations Analysis