As someone working on fractional integral inequalities, I read this paper with interest. The extension of Milne-type inequalities to conformable fractional operators is a timely contribution. However, after carefully checking the details, I believe there may be a normalization issue in Lemma 2 that could affect the scaling of the main results.
In Definition 2, the conformable fractional integral is defined with a factor of 1/Γ(β). Yet in the proof of Lemma 2 (equations (4) and (5)), the term
(2^βα+1 Γ(β+1))/(θ2−θ1)^(βα+1) appears alongside the operator βJ^α. Since Γ(β+1)=β Γ(β), this introduces an extra factor of β relative to the definition.
If this is not a typographical oversight, the identity in Lemma 2, and consequently all derived inequalities in Theorems 3-5 and their corollaries, might need rescaling. This is particularly relevant when α=β=1, where the results should reduce to known classical cases.
I would welcome clarification from the authors or others in the community. A quick re-derivation of the transformation from the γγ-integral to the conformable operator would help confirm whether the normalization is consistent.