General fractional integral inequalities for convex and m-convex functions via an extended generalized Mittag-Leffler function

Abstract

In this paper some new general fractional integral inequalities for convex and m-convex functions by involving an extended Mittag-Leffler function are presented. These results produce inequalities for several kinds of fractional integral operators. Some interesting special cases of our main results are also pointed out.

Minkowski’s inequality for the AB-fractional integral operator

“…The integral inequalities with Mittag-Leffler functions have been studied as a generalization of the classical inequalities. For instance, Farid et al [22] generalized several classical inequalities using an extended Mittag-Leffler function and evaluated particular cases of their results. More related work can be found in [23][24][25].…”

Generalized k-fractional integral inequalities associated with $(\alpha ,m)$-convex functions

“…5 Department of Mathematics, Air University, Islamabad, Pakistan. 6 Department of Mathematics, Government College University, Lahore, Pakistan. 7 Govt Boys Primary School Sherani, Hazro Attock, Pakistan.…”

Estimations of fractional integral operators for convex functions and related results

“…Let μ, α, l, γ , ν, c ∈ C, (μ), (α), (l) > 0, (c) > (γ ) > 0 with p ≥ 0, δ > 0 and 0 < k ≤ δ + (μ). Then the differential equation 16) with the initial condition (I 1-ν 0 + )(0+) = C, has a solution in the space L(0, ∞),…”