Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel
Pshtiwan Othman Mohammed, Thabet Abdeljawad
Abstract
Abstract At first, we construct a connection between the Atangana–Baleanu and the Riemann–Liouville fractional integrals of a function with respect to a monotone function with nonsingular kernel. By examining this relationship and the iterated form of Prabhakar fractional model, we are able to find some new Hermite–Hadamard inequalities and related results on integral inequalities for the two models of fractional calculus which are defined using monotone functions with nonsingular kernels.
Topics & Concepts
MathematicsInvertible matrixIterated functionKernel (algebra)Pure mathematicsMonotone polygonFractional calculusFunction (biology)Operator (biology)Hadamard three-lines theoremMittag-Leffler functionHermite polynomialsConnection (principal bundle)Hadamard productApplied mathematicsMathematical analysisHadamard transformGeometryBiochemistryEvolutionary biologyChemistryGeneTranscription factorRepressorBiologyMathematical Inequalities and ApplicationsFractional Differential Equations SolutionsNonlinear Differential Equations Analysis