Abstract

The main aim of this paper is to establish some new fractional integral inequalities of Grüss-type via the Saigo fractional integral operator.

Highlights

  • Gruss inequality is an inequality which establishes a connection between the integral of the product of two functions and the product of the integrals of the two functions

  • In literature few results have been obtained on some fractional integral inequalities using Hadamard fractional integral and Saigo fractional integral operator in [25, 26, 30– 32]

  • They are expected to lead to some applications for establishing uniqueness of solutions in fractional differential equations

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Summary

Introduction

Gruss inequality is an inequality which establishes a connection between the integral of the product of two functions and the product of the integrals of the two functions. Let f, g : [a, b] → R be two integrable functions such that φ ≤ f(x) ≤ Φ and γ ≤ g(x) ≤ Γ for all x ∈ [a, b]; φ, Φ, γ, and Γ are constant; . Many authors have studied the fractional integral inequalities via Caputo, Riemann-Liouville, and qfractional integral; see [6, 13–21]. Some authors have studied the Saigo fractional integral operator; for example, we refer the reader to [22–29] and references cited therein. In [19], Dahmani et al gave the following fractional integral inequality using Riemann-Liouville fractional integral. In literature few results have been obtained on some fractional integral inequalities using Hadamard fractional integral and Saigo fractional integral operator in [25, 26, 30– 32]. Our purpose in this paper is to establish some new results using Saigo fractional integral

Preliminaries
Grüss-Type Fractional Integral Inequality
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