Quadrature Rules for the Fm-Transform Polynomial Components
Round 1
Reviewer 1 Report
Report on axioms
Manuscript title: "Quadrature Rules for the Fm-transform Polynomial Components ".
Journal: axioms
There are some major comments considered as follows:
1- The paper should be reviewed linguistically and grammatically checked for the paper.
2- Add reference to equations 1, 2, and 7 in this paper.
3- Other functions must be taken into the results to support the results and theories.
4-The main idea of the study must be clarified.
5-The introduction should be reformulated in terms of the sequence and arrangement of literary ideas.
6- Future research direction most be shown in conclusion.
7- Write the physical significance of governing equations.
8-A comparison between the present results and previous investigations must add to show the new results obtained and their applications in Engineering and other topics.
Finally, I recommended the manuscript for publication in axioms after releasing the above points.
Author Response
We sincerely thank the reviewers for their careful reading and constructive suggestions. We carefully analyzed all the proposals and changed the text of the article, taking into account the comments made.
We respond to the comments in the attached file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this study, the efficient numerical methods that we can use to calculate the 1 higher-order F-transform components. The Gauss quadrature rules and the accuracy of 2 which depends on the number of integration points are examined. The 3- and 4-point Gaussian quadrature 3 rules and find all their parameters that allow us to obtain exact analytical expressions for the values 4 of definite integrals in which the integrands are polynomials up to (and including) 7th degree are analyzed. This that it possible to efficiently calculate the F-transform components of up to 3d degree. In addition, the applicability of the finding results to the numerical integration of arbitrary functions.
However, the manuscript needs some modification for a better presentation of work can be highlighted:
1-The novelty of the present work is not clear.
2- The introduction section needs to be improved by considering the recently published papers.
3- More numerical examples must be added.
4- There is no comparison b/w the derived results and results available in the literature.
Author Response
We sincerely thank the reviewers for their careful reading and constructive suggestions. We carefully analyzed all the proposals and changed the text of the article, taking into account the comments made.
We respond to the comments in the attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Accept in present form
Reviewer 2 Report
All comments are discussed. Now, I suggest by publication.
