A Review for “On Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives”

Submitted to Mathematics (MDPI)

Last updated October 7, 2019

The manuscript discusses the proof of existence results using there or four different approaches. The first time readers might think three, but the authors claimed there are four. Perhaps the authors could verify this one further.

The following provides some remark to the manuscript. 1. As mentioned above, clarify how many approaches are implemented in proving the existence results. 2. Explain what are the similarities and the differences between the first, the second, the third and the fourth approaches? 3. Why the uniqueness is not discussed in this situation? 4. What is the rationale when choosing examples in Section 4? For instance, why take zero for the first component in (12), while it is something else in (11)? 5. Some paragraphs need to be reworded and rewritten again as they are not clear to the reader. Please obtain help in professional English. For instance, paragraph one of the Introduction. 6. In Definition 1, q ∈ R is mentioned but it never appeared somewhere else earlier. What is q? 7. Please explain the meaning of Carathéodory or L1 -Carathéodory. This is a very specialized term that many readers are not aware of. 8. Likewise, the authors use many times the abbreviation of u.s.c. This is not listed in the common abbreviation list in mathematics. See for instance https://en.wikipedia.org/wiki/List_of_ mathematical_abbreviations. Or, please contribute the abbreviation to that Wikipedia page. 9. Please reformat (5). It is unclear to the readers. 10. How is it obvious that the fixed points V are solutions of the problem (2)? Explain! 11. Please add a reference to Arzelá-Ascoli theorem. 12. Please fix the typo on line 78. 13. Perhaps the authors meant Theorem 1 instead of Theorem 3.2? There is no Theorem 3.2 in the manuscript. 14. Is J ⊆ R? 15. What are the meaning of ‘equicontinuous sequence’ and ‘contraction’? 16. Is that Ψ1 instead of Ψ2 in line 123? 17. Please avoid double negative phrases in line 131. 18. Shouldn’t be 0 < δ < 1? 19. I think the style of reference list does not follow the MPDI format, the year should be boldface instead of the volume number. Please check, and if it is correct, please fix that.

The Second Review for “On Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives”

Submitted to Mathematics (MDPI)

Last updated October 31, 2019

We thank the authors for improving and updating the manuscript. The following gives a number of issues that can be incorporated. 1. The fourth author appears in the manuscript but he was absent in the message sent by the Editorial Office. 2. Please include the corporate email address, preferably from the authors’ current institution. 3. The abstract needs to be improved and reworded. Use active sentences instead of passive voice. 4. Line 28 is not necessary and not necessarily written with emphasis. Everybody knows that most of the published papers contain some new things. Otherwise, they cannot be published, right? Either remove it entirely or rewrite it nicely. 5. Should not be Lemma 1 referred to as Theorem from the previously published paper? If not (as long as the rationale is given), then leave it as it is. 6. Line 39: is not that ‘compact’ and ‘closed and bounded’ usually refer to the same thing? If not, then perhaps more clarification needs to be given. 7. Please provide references for Definition 3. 8. ‘Almost everywhere’ should not be abbreviated. 9. I could not find the correction to u.s.c. Where is it? 10. What is the meaning of Ω? Is that true that Ω = Ω ∪ ∂Ω? So, is that correct if the readers conclude that in this case, Ω is an open set? 11. In Lemma 2, is it D or D? The bar sign is too small and very easy to be overlooked by the readers. 12. Line 121: As. 13. Is it necessary to provide a reference for Definition 4? 14. ‘Acknowledgements’ and ‘Funding’ are redundant.