On Caputo Fractional Derivatives and Caputo–Fabrizio Integral Operators via (s, m)-Convex Functions
Ammara Nosheen, Maria Tariq, Khuram Ali Khan, Nehad Ali Shah, Jae Dong Chung
Abstract
This paper contains a variety of new integral inequalities for (s,m)-convex functions using Caputo fractional derivatives and Caputo–Fabrizio integral operators. Various generalizations of Hermite–Hadamard-type inequalities containing Caputo–Fabrizio integral operators are derived for those functions whose derivatives are (s,m)-convex. Inequalities involving the digamma function and special means are deduced as applications.
Topics & Concepts
MathematicsFractional calculusConvex functionHermite polynomialsRegular polygonPure mathematicsType (biology)Mathematical analysisGeometryBiologyEcologyMathematical Inequalities and ApplicationsFractional Differential Equations SolutionsIterative Methods for Nonlinear Equations