Spectral Collocation Approach via Normalized Shifted Jacobi Polynomials for the Nonlinear Lane-Emden Equation with Fractal-Fractional Derivative

Round 1

Reviewer 1 Report

Please consider  the attached file.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 1
Thanks a lot for your valuable comments.

Kindly Check The attached file.

Warm Regards

Author Response File: Author Response.pdf

Reviewer 2 Report

I have attached the review report.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 2
Thanks a lot for your valuable comments.

Kindly Check The attached file.

Warm Regards

Author Response File: Author Response.pdf

Reviewer 3 Report

Please see the attached for details.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 3
Thanks a lot for your valuable comments.

Kindly Check The attached file.

Warm Regards

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

After I checked the revised manuscript, I think that the authors almost make a satisfied revisions except several minor concerns, more precisely,

1) The second line of Abstract: I suggest the authors write "...singular Lane-Emden equations with..." as "...singular Lane-Emden (LE) equations with...", then the authors can use "LE" in the 7th line;

2) I suggest the Refs. [32,33] can be suitably cited in "... some other types of fractional and generalized fractional differential equations; see e.g., [32,33]." (see the last sentence of Section 6);

3) I suggest the authors define the $L_2$ and $L_\infty$ norm (see Sections 4-5) in the suitable place of this manuscript;

4) It seems that the authors can directly use "LE" rather than "Lane-Emden" in Sections 3-6;

5) The journal name of Ref. [17] should be "Numer. Funct. Anal. Optim.";

6) Ref. [31] should be "..., J. Sci. Comput. 2020, 83(1), 10. doi: 10.1007/s10915-020-01193-1".

In conclusion, I suggest the authors correct the above mentioned concerns.

Author Response

Dear Reviewer

Greetings

Really we are very indebted to your vital comments through the two rounds of revisions. We have responded to all your comments.

Thank you with much appreciation.

Regards,

Youssri

Author Response File: Author Response.pdf