Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace
Round 1
Reviewer 1 Report
The submitte manuscript evaluated the number of weak solutions for one-dimensional fractional N−Laplacian systems involving singular nonlinearities in the product of the fractional Orlicz-Sobolev spaces. Two results obtained that
1) these problems have at least one nontrivial solution under some conditions and 2) these problems have also infinitely many weak solutions on the same conditions.
Based on the evaluations, I think the quality is sufficient to meet the basic requirement of the journal and I think it can be considered for acceptance after a minor revision. I suggest the author add more literature review on the proposed topic and make some numerical discussion at the end of equations developments. Otherwise, the paper is not very readable for the potential readers of the journal.
Author Response
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The following major comments concerns should be considered in order to prepare a contribution that meets the level of the journal. The most important are listed below.
a- In Introduction, author described past work, but little comment on the contribution and shortcoming. Author need to provide critical comments.
b- Are we in a regime which could apply to a real physical system?
c- And how is this appropriate assumption is real applications?
d- The considered ranges of governing parameters should be justified. What is the reason for these ranges?
e- Nomenclature part with all used parameters should be included in the paper.
f- In order to verify the validity of current model, authors need to compare their results with reported experimental data and models in literatures.
- Important outcomes of the present study must be highlighted in the abstract.
- In Introduction, author described past work, but little comment on the contribution and shortcoming. Author need to provide critical comments.
- Paper is devoted to nanofluid flow, but there is no information about the considered nanofluid. Please, describe the used nanofluid with all physical properties for the base fluid and nanoparticles and what model has been applied for description of transport processes.
- The considered ranges of governing parameters should be justified. What is the reason for these ranges?
- And how is this appropriate assumption in real applications?
- The coefficients of the relations are very “bushy”. It is very difficult to check their correctness.
- The results and findings should be compared to and discussed in the context of earlier work in the literature.
- What conclusions can be drawn from the results? What is the novelty of the work and where does it go beyond previous efforts in the literature?
- Please include specific and quantitative results in your Abstract, while ensuring that it is suitable for a broad audience. References, figures, tables, equations and abbreviations should be avoided.
- Many mathematical formulas are expressed. The author should summarize them.
- The author must improve the References part with some articles that use identical schemes, to make the scheme used more plausible, for instance: 1. The Pramana - Journal of Physics, 93, Article number: 10 (2019).; 2. Advances in Difference Equations (2018) 2018:232:1-12.; 3. Journal of Electromagnetic Waves and Applications Vol. 31 (2017) 16, 1711–1721.; 4. Phys. Scr. 94 (2019) 055205 (7pp); Results in Physics, 9(2018) 1631-1634.;
Author Response
The authors upload the pdf file for the correction of the Reviewer 2's suggestion.
Author Response File: Author Response.pdf
Reviewer 3 Report
Please see the attached PDF.
Comments for author File: Comments.pdf
Author Response
The authors upload the pdf file for the correction of the Reviewer 3's suggestion
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The problems pointed out by the reviewer in the previous report have not been improved at all.
1) The problem of classical derivative is not even mentioned at all. This is not a response to the problem pointed out by the reviewer. It is a repetition of the same meaningless words.
2) The addition of a sentence to page 19 cannot be an explanation that the problem addressed in the paper is not "singular". As it is clear from the references cited in the introduction, the reason this nonlinear term is called singular is that it diverges near the boundary when considering solutions satisfying the homogeneous Dirichlet condition. Finding a solution in the loop space does not mean that you have solved a "singular" problem. It is just a sham.
I believe it is detrimental to the mathematical community for such documents to be published as peer-reviewed papers. I strongly recommend to reject the paper at this stage.
Author Response
please see the attachment.
Author Response File: Author Response.pdf
