Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case

Round 1

Reviewer 1 Report

The paper should be revised considerably, first of all, with respect to notations and explanations.

For example:

1. Page 1 (line 1 after Eq. (1)): what are D_L and D_M ? Moreover, to avoid a confusion with the notation of the derivative, these sets should be denoted in another way. 

2. Page 2 (line 4 od Sec. 2): it should be mentioned that "Gamma(beta)" is the Gamma-function.

3. Page 3  (line 1 in Lemma 1): on the previous page "Gamma" is used to denote the Gamma-function, but here it is used to denote the boundary of some set. By the way, what set is S_alpha,theta ?

4. Page 3 (line 4 in Lemma 1): on the previous pages "t" is a real nonnegative variable (time), but here it is a complex variable. What does it mean?

5. and so on!

The paper is completely unreadable.

Author Response

1.       We described in more detail the domains of operators (two lines after formula (1)) and changed the font in their denotations: ${\mathcal D}_L$ and ${\mathcal D}_M$ instead of $D_L$ and $D_M$.

2.       We changed the text according to your suggestion.

3.       The denotation of the contour $\Gamma$ is replaced by the denotation $\partial S_{\theta,a}$ in all the manuscript. The description of $S_{\theta_0,a_0}$ was given in line 49 on page 3. Now we added another description of $S_{\theta,a}$ before Lemma 1.

4.       It means that the $t$ can be real or complex depending on context. But now to avoid ambiguity we denote this complex variable by the symbol $\tau$ (see Lemma 1 and further).

5.       We carefully checked the entire manuscript for such flaws.

Thank you very much,

Authors.

Reviewer 2 Report

please see pdf of report

Comments for author File: Comments.pdf

Author Response

For Reviewer 2.

1.       We rewrite this place: “An approximate controllability criterion for the degenerate fractional order control system is obtained”.

2.       In the indicated phrases “which” is replaced by “whose”.

3.       In the Introduction after the first using of the notation for the H\”older functions space after formula (1) we added the phrase “where $C^\gamma([0,T];\mathcal Y)$ is the space of H\"older functions (see the definition before Theorem 1)”.

4.       We add “the” in this place.

5.       We corrected the sentence according to your suggestion.

6.       We changed the text according to your suggestion.

We carefully checked the entire manuscript for other flaws.

Thank you very much,

Authors.

Round 2

Reviewer 1 Report

The revised version looks much better. However, the conclusions section should be added.

Author Response

We added a Conclusion.

Thank you very much.