We extend the Montgomery identities for the Riemann-Liouville fractional integrals. We also use these Montgomery identities to establish some new integral inequalities. Finally, we develop some integral inequalities for the fractional integral using differentiable convex functions.
The aim of the present paper is to establish some fractional q-integral inequalities on the specific time scale, Ì t0 {t : t t 0 q n , n a nonnegative integer} ∪ {0}, where t 0 ∈ Ê, and 0 < q < 1.
IntroductionThe study of fractional q-calculus in 1 serves as a bridge between the fractional qcalculus in the literature and the fractional q-calculus on a time scale Ì t 0 {t : t t 0 q n , n a nonnegative integer} ∪ {0}, where t 0 ∈ Ê, and 0 < q < 1.Belarbi and Dahmani 2 gave the following integral inequality, using the RiemannLiouville fractional integral: if f and g are two synchronous functions on 0, ∞ , thenMoreover, the authors 2 proved a generalized form of 1.1 , namely that if f and g are two synchronous functions on 0, ∞ , thenfor all t > 0, α > 0, and β > 0.
In this paper, we establish a new weighted Ostrowski-type inequality for double integrals involving functions of two independent variables by using fairly elementary analysis.
Abstract:In this paper, we establish some new results related to the left-hand of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives are strongly s-convex functions in the second sense. Some previous results are also recaptured as a special case.
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