A Grüss Type Integral Inequality Associated With Gauss Hypergeometric Function Fractional Integral Operator

Abstract

Abstract. In this paper, we aim at establishing a generalized fractional integral version of Grüss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known results.

Grüss Type Inequalities for Variational Fractional Integral

“…In 2015, Choi and Purohit [8] obtained the general version of Theorem 1.5 which generalized the pervious results of Baleanu et al [7], Wang et al [28] and Tariboon et al [26].…”

“…Further information concerning the history and applications of some inequalities in fractional calculus can be found in [2], Azizollah Babakhani [7], [8], [10], [25], [25]- [28]. Recently, some inequalities of Grüss type for several kinds of fractional integrals have been established [7], [8], [10], [26]- [28]. For example, in 2010, Dahmani et al [10] proposed the following version of Grüss inequality for Riemann-Liouville fractional integral I α 0+ [.].…”

Some Grüss type inequalities involving generalized fractional operator

“…Using fractional integral operators, several developments of the classical inequalities, including (1), are studied by many authors, see [1,2,3,4,5,9,10,14,18] and references therein. In this direction, Dahmani et al [6] established a generalization of Grüss inequality by means of Riemann Liouville fractional integral operators.…”

Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals

“…with the condition that r −1 + s −1 = 1. Recently, by using fractional integral operators, several extensions of the classical inequalities, including Equation 5, have been studied by many authors, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24] and the references therein. We attempt to generate the inequality of Equation (5) by making use of the fractional integral operator of pathway type.…”