On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function
TLDR
In this article, the Hermite-Hadamard type inequalities involving fractional integrals with respect to another function were established, which generalize the Riemann-Liouville fractional integration and the Hadamard fractional integral integral.Abstract:
In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. c ©2016 All rights reserved.read more
Citations
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Hermite–Hadamard, Hermite–Hadamard–Fejér, Dragomir–Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals
TL;DR: These results allow a new class of functional inequalities which generalizes known inequalities involving convex functions to be obtained, and may act as a useful source of inspiration for future research in convex analysis and related optimization fields.
Journal ArticleDOI
Hermite-Hadamard type inequalities for F-convex function involving fractional integrals
TL;DR: Through the notion of F-convex, some new Hermite–Hadamard type and trapezoid type inequalities are found for the Riemann–Liouville fractional integrals and classical integrals.
Journal ArticleDOI
Hermite-Hadamard type inequalities for the generalized k-fractional integral operators.
TL;DR: Several Hermite-Hadamard type inequalities for the generalized k-fractional integral operators of a function with respect to another function are established.
Journal ArticleDOI
Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized Convex Functions
TL;DR: The authors approach the relationship that can be established between trapezoidal inequalities, generalized convex functions, and special functions, in particular with the so-called Raina function, which generalizes other better known ones such as the hypergeometric function and the Mittag–Leffler function.
Journal ArticleDOI
Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals
TL;DR: In this article, the authors established new Hermite-Hadamard type inequalities for harmonically convex functions via generalized fractional integrals, without using the harmonic convexity property for the functions.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Posted Content
Selected Topics on Hermite-Hadamard Inequalities and Applications
TL;DR: The Hermite-Hadamard double inequality for convex functions has been studied extensively in the literature, see as discussed by the authors for a survey of the Hermite Hadamard inequalities.
Journal ArticleDOI
Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities
TL;DR: An integral identity and some Hermite–Hadamard type integral inequalities for the fractional integrals are obtained and these results have some relationships with S.S. Dragomir and R.P. Agarwal's inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula.
Journal ArticleDOI
Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula
Sever S Dragomir,Ravi P. Agarwal +1 more
TL;DR: In this paper, two inequalities for differentiable convex mappings which are connected with the celebrated Hermite-Hadamard's integral inequality holding for convex functions are given.
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