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
Summary
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
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