Analogues to Lie Method and Noether’s Theorem in Fractal Calculus
Round 1
Reviewer 1 Report
The work is very interesting and has a subject of great relevance. We have the fractal calculus, on the other hand we have the Lie Method and Noether’s Theorem. I liked the work.
The work is interesting, and information that holds the reader's attention. But, I have some suggestion and considerations to improvement of this work. Some modifications are necessary, I listed below:
(1) After all the equation, there is a comma or a period mark. Please, verify all equations.
(2) The introduction (fourth-paragraph on "Fractional calculus" in the introduction) needs some references about recent applications of fractional operators. I will list a sequence of references on fractional calculus that will certainly help better the article, as well as attracting the attention of a different audience.
----- I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Academic Press, New York, 1998).
---- Approximate solutions to fractional subdiffusion equations. The European Physical Journal Special Topics, v. 193, n. 1, p. 229-243, 2011. APA
----- Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels. Fractal and Fractional, v. 2, n. 3, p. 20, 2018.
-----Fractional Prabhakar Derivative in Diffusion Equation with Non-Static Stochastic Resetting.Physics, 1(1), 40-58. (2019)
I liked very much,
Thank you for your attention.
Author Response
Dear Editor,
We are grateful to both referees for the thoughtful and careful evaluation of our work. In the revised manuscript all points from the reports of both referees are accounted as follows.
Response to the Report of referee 1:
The work is interesting, and information that holds the reader's attention. But, I have some suggestion and considerations to improvement of this work. Some modifications are necessary, I listed below:
After all the equation, there is a comma or a period mark. Please, verify all equations.
Thanks, I have done.
(2) The introduction (fourth-paragraph on "Fractional calculus" in the introduction) needs some references about recent applications of fractional operators. I will list a sequence of references on fractional calculus that will certainly help better the article, as well as attracting the attention of a different audience. I have added.
----- I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Academic Press, New York, 1998).
---- Approximate solutions to fractional subdiffusion equations. The European Physical Journal Special Topics, v. 193, n. 1, p. 229-243, 2011. APA
----- Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels. Fractal and Fractional, v. 2, n. 3, p. 20, 2018.
-----Fractional Prabhakar Derivative in Diffusion Equation with Non-Static Stochastic Resetting.Physics, 1(1), 40-58. (2019)
We hope that the revised manuscript meets the expectations of referees and is acceptable for publication.
Sincerely,
Dr. Alireza K. Golmankhaneh
Professor Cemil Tunc
Reviewer 2 Report
Please refer to the attached comments.
Comments for author File: 
Comments.pdf
Author Response
Dear Editor,
We are grateful to both referees for the thoughtful and careful evaluation of our work. In the revised manuscript all points from the reports of both referees are accounted as follows.
Response to the Report of referee 2:
This paper focuses on the Lie method and Noether’s Theorem in fractal Calculus. This topic is interesting and the paper is well written. In my opinion, this paper needs major revision, otherwise, it should be rejected. The following recommendations are for the authors to refer.
The background and motivation in the introduction part should be emphasized.
I have indicated in red.
More details might be needed for
I have added. One can see more details in references.
The contribution and innovation should be emphasized. Especially, what is the relationship between the two considered theme, i.e., Lie Method and Noether’s Theorem. I have indicated in red.
More simulation and discussion are expected to verify the developed theoretical results. I will do it in the future project
The potential applications of this work should be mentioned.
In the section of introduction I have mentioned
It is difficult to get the result in (7).
Thanks, I have revised and add more details.
Different line styles are expected for Figure 3 and more explanation is needed.
Thanks, I have corrected.
There are some grammar mistakes, such as the sentences before equations (7), (21), (23), (30), (40), etc.
I have revised the paper.
We hope that the revised manuscript meets the expectations of referees and is acceptable for publication.
Sincerely,
Dr. Alireza K. Golmankhaneh
Professor Cemil Tunc
