Hermite–Jensen–Mercer-Type Inequalities via Caputo–Fabrizio Fractional Integral for h-Convex Function
Miguel José Vivas Cortez, Muhammad Shoaib Saleem, Sana Sajid, Muhammad Sajid Zahoor, Artion Kashuri
Abstract
Integral inequalities involving many fractional integral operators are used to solve various fractional differential equations. In the present paper, we will generalize the Hermite–Jensen–Mercer-type inequalities for an h-convex function via a Caputo–Fabrizio fractional integral. We develop some novel Caputo–Fabrizio fractional integral inequalities. We also present Caputo–Fabrizio fractional integral identities for differentiable mapping, and these will be used to give estimates for some fractional Hermite–Jensen–Mercer-type inequalities. Some familiar results are recaptured as special cases of our results.
Topics & Concepts
MathematicsFractional calculusType (biology)Hermite polynomialsConvex functionDifferentiable functionRegular polygonApplied mathematicsPure mathematicsMathematical analysisBiologyEcologyGeometryMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsMathematical functions and polynomials