In the literature, several papers are devoted to inequalities of Simpson-type in the case of differentiable convex functions and fractional versions. Moreover, some papers are focused on inequalities of Simpson-type for twice differentiable convex functions. In this research article, we obtain an identity for twice differentiable convex functions. Then, we prove several fractional inequalities of Simpson-type for convex functions.

In this paper, we first obtain two weighted identities for twice partially differentiablemappings. Moreover, utilizing these equalities, we establish the weighted Herrmite-Hadamard typeinequalities and weighted Simpson type inequalities for co-ordinated convex functions in a rectangle from the plane R2, respectivelly. The results given in this paper provide generalizations of someresult established in earlier works.

This paper proves an equality for the case of twice-differentiable convex functions involving conformable fractional integrals. Using the established equality, we give new Simpson-type inequalities for the case of twice-differentiable convex functions via conformable fractional integrals. We also consider some special cases which can be deduced from the main results.

In this paper, some new interesting results based on quasi-geometrically convex mappings of both Hadamard’ s and Simpson’ s inequalities have been constructed defining a new identity for twice differentiable mappings.

In this paper, we present a general version of operator Bell-man inequality. Also, the refinement of inequality due to J. Aujla and F. Silva for the convex functions is given as well.

The aim of inequalities is to develop tools for analyzing the problems in pure and applied mathematics. Our primary objective in this research is to introduce some new type inequalities connected with Caputo fractional derivative. In the light of the operator, we extend and generalize some important inequalities to this fractional calculus dealing with synchronous functions.

Hardy–Sobolev–type inequalities associated with the operator L := x .Ñ are established, using an improvement to the Sobolev embedding theorem obtained by M. Ledoux. The analysis involves the determination of the operator semigroup {e_tL*L} t>0.

In this paper, we establish new cebysev type integral inequalities involving functions whose derivatives belong to Lp spaces via certain integral identities.