The Boundary Value Problem with Stationary Inhomogeneities for a Hyperbolic-Type Equation with a Fractional Derivative
Round 1
Reviewer 1 Report
Check the comma and the punctuation in the text and at the ends of the equations.
The author should give more importance to this work and update some recent references.
Author Response
Dear reviewer!
I thank you for your remarks. These comments undoubtedly contributed to the improvement of the article.
I corrected all the indicated errors, typos and shortcomings.
Sincerely, Ludmila Kirianova.
Reviewer 2 Report
The paper presents an analytical solution of a partial differential equation of hyperbolic type, containing both second-order partial derivatives and fractional derivatives of order below the second. Examples of polymer concrete under loading are considered.
My comments are as follows:
- The introduction must be improved. The content in Section 4 must go into the Introduction and explained what was presented in references [3] and [4] by the author and what is the novelty of the present paper. Also, the works [11] and [12] must be discussed since a direct reference to them is made. Finally, the author should provide a sufficient background on the subject and corresponding references must be included.
- Equations must be checked carefully. For example, equations between lines 40-41, 58-59, 62-65, 70-71, 73-74, 64-65, etc. are in error.
- Formulas and other mathematical concepts must be explained to make the paper self-contained so there is no need to read or consult the other author’s papers.
- Equations must end with a dot or comma.
- In the last section, Section 4, the findings in the previous sections must be explained and to state the main contribution of the paper.
In summary, the paper contains errors, and it is not complete.
Author Response
Dear reviewer!
I thank you for your remarks. These comments undoubtedly contributed to the improvement of the article.
I corrected all the indicated errors, typos and shortcomings.
Sincerely, Ludmila Kirianova.
Reviewer 3 Report
The author in this manuscript presents an analytical solution of a partial differential equation of hyperbolic type, containing both second-order partial derivatives and fractional derivatives of order below the second. In addition, interesting examples of the application of the results to the modeling of the behavior of polymer concrete under the action of loads are included. Trying to contribute to the improvement of the document presented, I would like to make some comments.
(i) (i) I think the introduction to this study is too concise. I miss a greater contextualization from the theoretical point of view, as well as from the field in which the results presented will be applied.
(ii) Although section 2 adequately poses the problem and establishes the solution method in good detail, I think that, with the reader in mind, some preliminaries on which the developed results are based should be briefly included.
(iii) Section 3 contains three interesting examples that illustrate the results obtained. supported by tables and figures.
(iv) In section 4, the author relates these new results with those obtained in references [3], [4], [11] and [12], either because they represent a generalization or because of the concordance of the precision level . This would be a discussion of the results, not the conclusions of a research paper. For this reason, I propose the author to extend his conclusions to other aspects, such as: possible lines of research from a theoretical point of view or possible new fields of application of these methods, for example. I believe that this could reveal the potential of the study carried out.
Author Response
Dear reviewer!
I thank you for your remarks. These comments undoubtedly contributed to the improvement of the article.
I corrected all the indicated errors, typos and shortcomings.
Sincerely, Ludmila Kirianova.
Round 2
Reviewer 2 Report
The revised version of the manuscript it seems to be fine.
I have no further comments.
