Pshtiwan Othman Mohammed

Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a c

Abstract The primary objective of this research is to establish the generalized fractional integral inequalities of Hermite-Hadamard-type for MT -convex functions and to explore some new Hermite-Hadamard-type inequalities in a form of Riemann-Liouville fractional integrals as well as classical integrals. It is worth mentioning that our work generalizes and extends the results appeared in the literature.

Integral inequalities play a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods. Thus, the present days 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. There is a strong relationship between convexity and symmetry. Whichever one we work on

In this article, we have established new Hermite–Hadamard's type inequalities for Riemann–Liouville fractional integrals of convex functions with respect to increasing functions. Our obtained inequalities generalize some recent obtained inequalities in the literature involving classical integrals and Riemann–Liouville fractional integrals. Finally, applications of our work are demonstrated via the known special functions of real numbers.

It is a familiar fact that inequalities have become a very popular method using fractional integrals, and that this method has been the driving force behind many studies in recent years. Many forms of inequality have been studied, resulting in the introduction of new trend in inequality theory. The aim of this paper is to use a fuzzy order relation to introduce various types of inequalities. On the fuzzy interval space, this fuzzy order relation is defined level by level. With the help of this r

Abstract We consider the modified Hermite–Hadamard inequality and related results on integral inequalities, in the context of fractional calculus using the Riemann–Liouville fractional integrals. Our results generalize and modify some existing results. Finally, some applications to special means of real numbers are given. Moreover, some error estimates for the midpoint formula are pointed out.

Abstract At first, we construct a connection between the Atangana–Baleanu and the Riemann–Liouville fractional integrals of a function with respect to a monotone function with nonsingular kernel. By examining this relationship and the iterated form of Prabhakar fractional model, we are able to find some new Hermite–Hadamard inequalities and related results on integral inequalities for the two models of fractional calculus which are defined using monotone functions with nonsingular kernels.

Abstract In this article, the notion of interval-valued preinvex functions involving the Riemann–Liouville fractional integral is described. By applying this, some new refinements of the Hermite–Hadamard inequality for the fractional integral operator are presented. Some novel special cases of the presented results are discussed as well. Also, some examples are presented to validate our results. The established outcomes of our article may open another direction for different types of integral in

In this study, the family <i>F</i> and <i>F</i>-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite-Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are <i>F</i>-convex. We also show that through the notion of <i>F</i>-convex we can find some new Hermite-Hadamard type and trapezoid type inequalities for the Riemann-Liouville fractio

In this study, by using a new identity we establish some new Simpson type inequalities for differentiables–convex functions in the second sense. Various special cases have been studied in details. Also, in order to illustrate the efficient of our main results, some applications to special means and weighted Simpson quadrature formula are given. The obtained results generalize and refine certain known results. At the end, a brief conclusion is given as well.

In this study, a few inequalities of Hermite–Hadamard type are constructed via the conformable fractional operators so that the normal version is recovered in its limit for the conformable fractional parameter. Finally, we present some examples to demonstrate the usefulness of conformable fractional inequalities in the context of special means of the positive numbers.

Fractional integral inequality plays a significant role in pure and applied mathematics fields. It aims to develop and extend various mathematical methods. Therefore, nowadays we need to seek accurate fractional integral inequalities in obtaining the existence and uniqueness of the fractional methods. Besides, the convexity theory plays a concrete role in the field of fractional integral inequalities due to the behavior of its definition and properties. There is also a strong relationship betwee

This study investigates the h ‐fractional difference operators with h ‐discrete generalized Mittag‐Leffler kernels ( in the sense of Riemann type (namely, the A B R ) and Caputo type (namely, the A B C ). For which, we will discuss the region of convergent. Then, we study the h ‐discrete Laplace transforms to formulate their corresponding A B ‐fractional sums. Also, it is useful in obtaining the semi‐group properties. We will prove the action of fractional sums on the A B C type h ‐fractional di

In this paper, we introduce the notion of MT-convex functions on co-ordinates and establish some new integral inequalities of Hermite-Hadamard type for MT-convex functions on co-ordinates on a rectangle Δ in the plane R2. Keywords: Hermite-Hadamard type inequality, Differentiable co-ordinated convex functions, 2010 Mathematics Subject Classification: 26D15, 26A51, 26A33, 26A42