Refinements of two fractional versions of Hadamard inequalities for Caputo fractional derivatives and related results
Ghulam Farid, Atiq ur Rehman, Sidra Bibi, Yu‐Ming Chu
Abstract
The aim of this paper is to study the fractional Hadamard inequalities for Caputo fractional derivatives of strongly convex functions. We obtain refinements of two known fractional versions of the Hadamard inequality for convex functions. By applying identities for Caputo fractional derivatives we get refinements of error bounds of these inequalities. The given results simultaneously provide refinements as well as generalizations of already known inequalities.
Topics & Concepts
Hadamard transformFractional calculusMathematicsConvex functionRegular polygonInequalityHadamard's inequalityPure mathematicsHadamard three-lines theoremMittag-Leffler functionApplied mathematicsMathematical analysisHadamard productHadamard matrixGeometryMathematical Inequalities and ApplicationsApproximation Theory and Sequence SpacesFractional Differential Equations Solutions