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.

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.

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.

In this paper, we present new integral results on frac-tional order inequalities involving convex functions using Marichev-Saigo-Maeda integral operators. Using the same integral approach, other Fractional integral inequalities for positive and continuous func-tions are also proved. The obtained results can be seen as a new con-tribution in inequality theory by means of Marichev-Saigo-Maieda ap-proach.

In this paper, we establish Hadamard type Fractional integral inequalities for a more general class of functions that is the class of (h _ m)_convex functions. These results are due to Riemann-Liouville (RL) k-Fractional integrals: a generalization of RL Fractional integrals. Several known results are special cases of proved results.

In this study, we established the Hermite-Hadamard type, Simpson type, Ostrowski type and midpoint type integral inequalities for the s-convex functions in the second sense via Katugampola Fractional integrals. By using Katugampola Fractional integral operators, we obtained several new identities and presented new results for the s-convex function in the second sense. We made connections of our results with various results recognized in the literature. Finally, applications to special means are examined to verify the efficiency of the established results.

In this paper, new generalized variants of Ostrowski’s type identities involving the Atangana-Baleanu-Katugampola Fractional integral operator for differentiable convex and twice differentiable convex functions are presented. Using these equalities or lemmas along with several known identities, new inequalities for convex functions and the Atangana-Baleanu-Katugampola, Fractional integral operators are proved. By making appropriate choices of parameters, some connections between our results and various other findings are also recognized in the paper. Finally, some applications to unique means for positive real numbers are offered.

New variants of the Hermite - Hadamard inequality within the framework of generalized Fractional integrals for $(h,m,s)$-convex modified second type functions have been obtained in this article. To achieve these results, we used the Holder inequality and another form of it - power means. Some of the known results described in the literature can be considered as particular cases of the results obtained in our study.

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 article, we obtain generalizations for Gruss type integral inequality by using h (x) -Riemann-Liouville Fractional integrals.