Some Grüss-type inequalities using generalized Katugampola fractional integral

Abstract

The main objective of this paper is to obtain generalization of some Grusstype inequalities in case of functional bounds by using a generalized Katugampola fractional integral.

Certain fractional integral inequalities using generalized Katugampola fractional integral operator

“…In the literature, some fractional inequalities are obtain by using Generalized Katugampola fractional integral, see [1,4,14,18]. Motivated by above work in this paper we have obtain some new inequalities using generalized Katugampola fractional integral for convex functions.…”

“…Here, we devoted to basic concepts of Generalized Katugampola fractional integral,see [1,13,20]. Definition 2.1.…”

“…Remark 2.3. The fractional integral (2.1) contain five wellknown fractional integral as its particular cases, see [1,13,20] 1. Setting k = 0, η = 0, a = 0 and taking the limit ρ → 1 in (2.1), the integral operator (2.1) reduces to the Riemann-Liouville fractional integral.…”

Grüss-type fractional inequality via Caputo-Fabrizio integral operator

“…Chinchane and Pachpatte [10], investigated some new fractional integral inequalities of the Grüss-type by considering the Saigo fractional integral operator. In [1,21,34,35,36] authors obtained some the Grüss-type inequalities by using different types of fractional integral operators. Fractional calculus is generalization of traditional calculus into non-integer differential and integral order.…”

A note on some Ostrowski type inequalities via Generalized Exponentially Convexity

“…The terms convexity and inequalities have a wide range of applications in the growth of variants branches of pure and applied mathematics as well as in different areas of pure and applied sciences. The initiative works and significant contributions of these two terminologies can be found in the literature, see the references [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. In 1938, Ostrowski [18], developed a significant integral inequality connected with differentiable functions.…”