Further Hermite–Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors 1. What is the main question addressed by the research?   Versions of Hermite-Hadamard, midpoint-and trapezoid-type inequalities involving fractional integral operators with exponential kernels.   2. What parts do you consider original or relevant for the field? What
specific gap in the field does the paper address?   Inequalities with remainder terms. The paper generalizes existing results.   3. What does it add to the subject area compared with other published
material?   Remainder terms which show up with fractional integral operators with exponential kernels.   4. What specific improvements should the authors consider regarding the
methodology? What further controls should be considered?   For consistency, the authors have to change f to A on p. 1.   5. Please describe how the conclusions are or are not consistent with the
evidence and arguments presented. Please also indicate if all main questions
posed were addressed and by which specific experiments.   In the proofs, the authors indicate the calculations. More specifically, they have details to aid their arguments. Also, they have examples which underscore their main theorems and in some way highlight their remainder terms (e.g. the exponential function is convex and has a convex derivative, with this, they can explicitly graph their range for the parameter).

6. Are the references appropriate?   They are.   7. Please include any additional comments on the tables and figures and
quality of the data.

The graphs are useful.

 

Author Response

Please see the attachment for the corrections details.

Thank you

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Comments for author File: Comments.pdf

Author Response

Please see the attachment for the corrections details.

Thank you

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper introduces new versions of Hermite-Hadamard, midpoint- and trapezoid-type inequalities involving fractional integral operators with exponential kernels, as proposed by Ahmad et al. in \cite{kir}. We explore these inequalities for differentiable convex functions and demonstrate their connections with classical integrals. The paper also validates the derived inequalities through numerical example with graphical representations. Some important revisions are required.. 1.write abstract in proper ways, so that it contains the main contributions. It's too short. 

2. Write tha organization of the paper in a separate subsection. 

3. Introduction is too short. Give research background, literature review. Cite more references related to the work. Compare these paper with your work. 

4. Write some sentences at the start of each section, what are given here. 

5. Give another example and describe this, with main importance. 

6. Give some limitations and future works in conclusion. 

 

Author Response

Please see the attachment for the corrections details.

Thank you

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have corrected the whole manuscript according to my suggestions. The new version is accepted for publication.