Abstract The fractional structures of variables using Riemann–Liouville notion have been analyzed by various authors. novel idea this article is to introduce the new weighted behavior on random integral inequalities. In view these, we obtain some generalized inequalities integration continuous variables.

In this paper, we give Hermite–Hadamard type inequalities of the Jensen–Mercer for Riemann–Liouville fractional integrals. We prove integral identities, and with help these identities some other eminent inequalities, such as Jensen, Hölder, power mean obtain bounds difference newly obtained inequalities.

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract This paper investigates a boundary value problem of Caputo type sequential fractional differential equations supplemented with nonlocal Riemann-Liouville f...

In this paper we establish new Hermite-Hadamard type inequalities involving fractional integrals with respect to another function. Such fractional integrals generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. c ©2016 All rights reserved.

We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fraction...

Some new weakly singular integral inequalities are established by a method, which generalize some results of this type in previous papers. By these inequalities, we present the attractivity solutions for Riemann–Liouville fractional differential equations. Finally, several examples given to illustrate our main results.

Fractional integral operators are useful tools for generalizing classical inequalities. Convex functions play very important role in the theory of mathematical This paper aims to investigate Hadamard type inequalities a generalized class namely strongly (α,h−m)-p-convex by using Riemann–Liouville fractional integrals. The results established this give refinements various well-known which have b...