Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

Round  1

Reviewer 1 Report

The paper is well written and it is only recommended to provide more examples in the last section if applicable. Also, the discussion part needs more elaboration. 

Author Response

Sir,

Results and methodology are improved. Made subsequent changes in conclusion

Reviewer 2 Report

The article is very interesting, but I think it's needed to have a definition table for all variables to understand the concept of paper, all Eq. required to have a number, for example, look at page 2 of this paper https://arxiv.org/pdf/1704.07468.pdf?fname=cm&font=TypeI paper,

Author Response

Sir,

1) We prepare definition table for all variables to understand the concept of paper,

2) all Eq.  have a number now.

Reviewer 3 Report

The article presents the existence of PC-mild solutions for non-local fractional  impulsive functional integro-differential equations with finite delay. In my opinion, the article presents a new and interesting method. Nevertheless, the authors should carefully revise the editing to improve paper readability. The presentation is clear and correct. However, the conclusion should be written in detail by stressing the importance of the proposed method with some application scenarios. It would greatly benefit the reader if the author could provide more information on why the proposed results should be considered efficient, and under which application's scenario these results are superior.

Author Response

Sir, We made following changes in the manuscript:

1) We carefully revise the editing to improve paper readability.

2) The conclusion is modified and is now written in detail by stressing the importance of the proposed method with some application scenarios.

3) For benefit the reader we have provided more information on why the proposed results should be considered efficient, and under which application's scenario these results are superior.

Reviewer 4 Report

Based on the submitted paper draft, I think that the following issues should be addressed:

- please explain the "PC-mild" before using it in the abstract;

- please make the abstract section more concrete, suggesting to which extent the results have been extended, if possible, add a quantitative approach to the improvement;

- please go more into depth and present some key characteristics of the references mentioned in row 19. There are too many references one should cobsult, thus I think it is better to highlight some of their main characteristics considered in their research, such us one can easily choose which one to consult, if interested;

- the references in rows 27 and 28 divide them into the mentioned categories, so one can easily access the ones he/she needs;

- please explain the variables used in equations;

- can you please also add a numerical example?;

- I am not sure about the improvents and ectension of the results you mentioned in the abstract. Please add a discussion section in which you demonstrate these improvements;

- give some practical explamples of situations in which the presented cases may arrise.

Thank you!

Author Response

Sir,

 following changes have been done as per your suggestions:

1) Full form of  "PC-mild" before using it in the abstract;

2)  abstract section is now more concrete, suggesting to which extent the results have been extended.

3) We removed few of the references form the bibliography and highlight some of their main characteristics considered in their research, so that one can easily choose which one to consult.

4) variables used in equations  are explained

5) numerical example is added.

6) Importance of the result has been mentioned.

Thanks and regards,

Reviewer 5 Report

Authors should improved the paper in the following way: (i) Split up the introduction section. Write motivation, novelties as a subsection and also the structures of the paper (ii) The paper is like.....theorem, theorem....Any author can find interest on it. Format the paper for its better presentation. (iii) If possible give an application of your work or at least mention where you can apply it (iv) Highlighted the main contribution on clonclustion

Author Response

Sir, Following changes have been done as per your instruction:

 (i) We Split up the introduction section. Wrote motivation, novelties as a subsection and also the structures of the paper

  (ii) an application of the work or at least  where we can apply it ...is mentioned

(iii) Main Contribution is highlighted in the conclusion.

Thanks and regards,

Prof. D. N. Chalishajar