Ostrowski-type fractional integral inequalities for mappings whose derivatives are h-convex via Katugampola fractional integrals

Abstract

In this paper we generalize some Riemann-Liouville fractional integral inequalities of Ostrowski-type for h-convex functions via Katugampola fractional integrals, generalizations of the Riemann-Liouville and the Hadamard fractional integrals. Also we deduce some known results by using p-functions, convex functions and s-convex functions.

Generalized Ostrowski-type inequalities involving second derivatives via the Katugampola fractional integrals

“…For more information about the Katugampola fractional integrals and related results, we refer the interested reader to the papers [5,11,12,14,15,22].…”

“…For more information about the Ostrowski inequality and its associates, we refer the interested reader to the papers [1, 2, 6-9, 11-13, 21]. The authors in [1,[11][12][13]21] provided some Ostrowski-type inequalities for some classes of convex functions.…”

OSTROWSKI-TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR r−TIMES DIFFERENTIABLE h−CONVEX FUNCTIONS

“…In 1938, A. M. Ostrowski proved an interesting integral inequality, estimating the absolute value of the derivative of a differentiable function by its integral mean as follows: Theorem 1.1. [6] Letf : I → R, I is an interval in R, be a differentiable function in I o , the interior of I and µ, ν ∈ I o , µ < ν. If |f (u)| ≤ M for all u ∈ [µ, ν], then…”

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The authors have tried to prove some Ostrowski-type fractional integral inequalities for r−times differentiable functions and generalized some results which were carried out in both [6,25]. Some applications to special means are given.

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Fractional Ostrowski Type Inequalities via Generalized Mittag–Leffler Function

“…Fractional integral operators also play a vital role in the advancement of classical mathematical inequalities. For example, Hadamard inequality, Ostrowski inequality, Gruss inequality, and many others have been presented for fractional integral and derivative operators, see [7][8][9][10][11][12][13][14][15][16]. e aim of this paper is to study well-known Ostrowski inequality for an integral operator which is directly associated with many fractional integral operators defined in near past.…”