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, we use Hadamard FRACTIONAL INTEGRAL to establish some new INTEGRAL inequalities of Gruss type by using one or two parameters. Furthermore, other INTEGRAL inequalities of reverse Minkowski's type are also obtained.

In this paper, we , rst establish two new identities for differentiable function involving generalized FRACTIONAL INTEGRALs. Then, by utilizing these equalities, we obtain some midpoint type inequalities involving generalized FRACTIONAL INTEGRALs for mappings whose derivatives in absolute values are convex. We also give several results as special cases of our main results.

INTEGRAL and differential of FRACTIONAL order are important notion that is often used in dealing with Frechet geometry. Based on pseudo-operations given by monotone and continuous function g, we study pseudo-derivative and pseudo-INTEGRAL of FRACTIONAL order through this paper.

In the present work, FRACTIONAL calculus is used to establish new INTEGRAL inequalities for the FRACTIONAL moments of continuous random variables. Generalizations of some classical INTEGRAL inequalities are also obtained.

This paper deals with the solution of a class of Volterra INTEGRAL equations in the sense of the conformable FRACTIONAL derivative. For this goal, the well-organized Neumann method is developed and some theorems related to existence, uniqueness, and sufficient condition of convergence are presented. Some illustrative examples are provided to demonstrate the efficiency of the method in solving conformable FRACTIONAL Volterra INTEGRAL equations.

In this paper, we have obtained weighted versions of Ostrowski, Č ebysev and Grü ss type inequalities for conformable FRACTIONAL INTEGRALs which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.