In this paper, some new estimates on Fej?r sort inequalities via Riemann Liouville fractional integral for the products of two harmonically-convex functions are obtained.

In this paper we continue our investigation of multivariable integral inequalities of the type considered by Hilbert and recently by Pachpatte by focusing on fractional derivatives. Our results apply to integrable not necessarily continuous functions, and we are able to relax the original conditions to admit negative exponents in the weight functions. Mathematics Subject Classification: 26A33, ...

We give a short summary of Varopoulos’ generalised Hardy-LittlewoodSobolev inequality for self-adjoint C0 semigroups and give a new probabilistic representation of the classical fractional integral operators on Rn as projections of martingale transforms. Using this formula we derive a new proof of the classical Hardy-LittlewoodSobolev inequality based on Burkholder-Gundy and Doob’s inequalities...

With this study, several useful results consisting of certain applications of the fractional differ-integral operators to certain multivalent functions are first determined and a few useful consequences of them between certain equations and inequalities relating to multivalently functions which are analytic in the unit open disk are then pointed out.

This paper deals with some multidimensional integral operators involving the Gauss hypergeometric function in the kernel and generating the multidimensional modified fractional calculus operators introduced in [8]. Some mapping properties, weighted inequalities, a formula of integration by parts and index laws are obtained.

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.

We establish some sharp maximal function inequalities for the Toeplitz type operator, which is related to certain fractional singular integral operator with general kernel. These results are helpful to investigate the boundedness of the operator on Lebesgue, Morrey and Triebel–Lizorkin spaces respectively.

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works.

*Correspondence: [email protected] 1Luleå University of Technology, Luleå, 971 87, Sweden 2Narvik University College, P.O. Box 385, Narvik, 8505, Norway Full list of author information is available at the end of the article Abstract We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n ∈ N. Some new Hardy-type inequalities for this operator are proved and dis...

In this article, we get solutions of some integral inequalities Hermite-Hadamard type and using the approach ($\psi$,$h$)-Convex function by way Riemann-Liouville Fractional integrals Katugampola operators.