fractional integral operators play an important role in generalizations and extensions of various subjects of sciences and engineering. This research is the study of bounds of Riemann-Liouville fractional integrals via (h 􀀀,m)-convex functions. The author succeeded to , nd upper bounds of the sum of left and right fractional integrals for (h􀀀, m)-convex function as well as for functions which are deducible from aforementioned function (as comprise in Remark 1. 2). By using (h 􀀀,m)-convexity of jf′, j a modulus inequality is established for bounds of Riemann-Liouville fractional integrals. Moreover, a Hadamard type inequality is obtained by imposing an additional condition. Several special cases of the results of this research are identi, ed.

In this paper, it is aimed to improvement the boundaries of fractional integral operators containing extended generalized Mittag-Leffler functions. The offered results enhance the previously known bounds of the distinct fractional integral operators for strongly $p$-convex functions of higher order. The acquired inequalities ensure boundedness, continuity, and Hadamard type inequality for fractional integrals containing an expanded Mittag-Leffler function. Furthermore, these results can be refined for various classes of strongly convex functions offered in the literature.

In the present work, we prove a parametrized identity for a di erentiable function via generalized integral operators. By applying the established identity and the new so{called generalized m-convex function, some generalized trapezium, Ostrowski and Simpson type integral inequalities have been discovered. Various special cases have been studied as well. Some applications of the present results to special means and new error estimates for the trapezium and midpoint quadrature formula have been investigated. It is hoped that the methods and techniques of this paper could further stimulate the research conducted in the  eld of integral inequalities.

In this paper, we establish sharp maximal function inequalities for the Toeplitz type operator related to some general fractional integral operators. As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces. The operators include Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

In this article, we present a new fractional integral with a non-singular kernel and by using Laplace transform, we derived the corresponding fractional derivative. By composition between our fractional integration operator with classical Caputo and Riemann-Liouville fractional operators, we establish a new fractional derivative which is interpolated between the generalized fractional derivatives in a sense Riemann-Liouville and Caputo-Fabrizio with non-singular kernels. Additionally, we introduce the fundamental properties of these fractional operators with applications and simulations. Finally, a model of Coronavirus (COVID-19) transmission is presented as an application.

We consider two general integral operators where are the extensions of the Kim-Merkes operator and Pfaltzgraff operator. We will proved in this paper the univalent conditions for these operators when we make some restrictions about the functions from your definitions.

Weighted integral inequalities for general integral operators on monotone positive functions with parameters $p$ and $q$ are established in [4]. The aim of this work is to extend the results to different cases of these parameters, in particular for negative $p$ and $q$. We give some new lemmas which will be frequently used in the proofs of the main theorems.