Abstract
This article investigates new inequalities for generalized Riemann–Liouville fractional integrals via the refined (alpha ,h-m)-convex function. The established results give refinements of fractional integral inequalities for (h-m)-convex, (alpha ,m)-convex, (s,m)-convex, and related functions. Also, the k-fractional versions of given inequalities by using a parameter substitution are provided.
Highlights
The origin of fractional calculus goes far back to the seventeenth century, when G.W
We considered the Riemann–Liouville fractional integrals with monotonically increasing function that plays a crucial role in our study
Corollary 1 Under the assumption of Theorem 6, the following fractional integral inequality holds for the refined (α, m)-convex function: 22α (2α – 1) f a + mb 2
Summary
The origin of fractional calculus goes far back to the seventeenth century, when G.W. If f is a tgs-convex function on [a, b], the following fractional integral inequality holds: 2f a +2 b ≤ 2((bμ–+a1)μ) Iaμ+ f (b) + Ibμ– f (a) ≤ (μμ[f+(a1))(+μf+(b2)])
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