Fractional Weighted Ostrowski-Type Inequalities and Their Applications

Abstract

An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results.

Ostrowski-type inequalities pertaining to Atangana–Baleanu fractional operators and applications containing special functions

“…Ahmad et al [16], established some novel generalization of the Ostrowski inequality via an Atangana-Baleanu fractional operator for differentiable convex functions. To acquire detailed information about recent advancements of the Ostrowski-type inequality, we direct the readers to the following references (see [17][18][19][20]).…”

New Fractional Mercer–Ostrowski Type Inequalities with Respect to Monotone Function

“…In the same year, Yildirim and Kirtay [21] used the generalized Riemann-Liouville F-I to establish new variants for Ostrowski inequalities. Some recent development about weighted Ostrowski fractional inequalities can be observed in [22].…”

NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR $k$-$\beta $-CONVEX FUNCTIONS VIA GENERALIZED $k$-FRACTIONAL CONFORMABLE INTEGRAL OPERATORS

“…Since the discovery of this inequality, many researchers have given considerable attention to study of inequalities in generale in real, fractional and quantum cases see [5,6,7,8,9,11,12,14,15,20,24,25,27,28,29,30,34,39,40].…”