Some new Chebyshev and Grüss-type integral inequalities for Saigo fractional integral operators and their q-analogues

CHEBYSHEV TYPE INEQUALITIES FOR THE SAIGO FRACTIONAL INTEGRALS AND THEIR q–ANALOGUES

The aim of the present paper is to obtain certain new integral inequalities involving the Saigo fractional integral operator. It is also shown how the various inequalities considered in this paper admit themselves of q -extensions which are capable of yielding various results in the theory of q -integral inequalities. Mathematics subject classification (2010): 26D10, 26A33, 05A30.

Some generalized Ostrowski-Grüss type integral inequalities

Some new Hardy-type inequalities for Riemann-Liouville fractional q-integral operator

*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...

Certain Inequalities Involving Generalized Erdélyi-Kober Fractional q-Integral Operators

In recent years, a remarkably large number of inequalities involving the fractional q-integral operators have been investigated in the literature by many authors. Here, we aim to present some new fractional integral inequalities involving generalized Erdélyi-Kober fractional q-integral operator due to Gaulué, whose special cases are shown to yield corresponding inequalities associated with Kobe...

Some Weighted Integral Inequalities for Generalized Conformable Fractional Calculus

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss 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.