An Approximate Solution of the Time-Fractional Two-Mode Coupled Burgers Equation

Round 1

Reviewer 1 Report

Report on “AN APPROXIMATE SOLUTION OF THE TIME-FRACTIONAL TWO-MODE COUPLED BURGERS EQUATION”

 

    In the paper, authors solved time-fractional two-mode coupled Burgers equation  with the Caputo fractional derivative.  Further, they applied the modified homotopy perturbation method coupled with Laplace transform (He-Laplace method) to find its aproximate analytical solution. Some example and results  from the main results are also discussed.   I feel that paper is interesting and may be publish in the Fractional and Fractals after following modifications

• Definition 1 and Definition 2 must contain integrability of the functions. Is it integrable over all R ? such property should be included in the definitions.
• I did not find any use of Lemma 1 in the whole paper. It be must removed.
• Please check paper thoroughly. Punctuation, comma etc need to be applied in some equations.
• Some references should be added to update the bibliograph

 

Author Response

• Definition 1 and Definition 2 must contain integrability of the functions. Is it integrable over all R ? such property should be included in the definitions.

        Corrected. 

• I did not find any use of Lemma 1 in the whole paper. It be must removed.

           Removed 

• Please check paper thoroughly. Punctuation, comma etc need to be applied in some equations.

          Corrected 

• Some references should be added to update the bibliograph  

        updated 

Reviewer 2 Report

Dear Editor

Please see the attachment file

Comments for author File: Comments.pdf

Author Response

1) This paper is actually to use a modification of the homotopy perturbation method, it is generally called as the fractional homotopy perturbation method. So an additional section is needed where a brief introduction to the homotopy perturbation method and the fractional homotopy perturbation method are elucidated.

Basically, we used Laplace transform homotopy perturbation method.  Since this method is already available in the literature. Due to avoid repetition, we use the scheme in our main results. 

2) Why are there so many definitions of fractional derivatives (Caputo, Caputo-Fabrizo, ... ) and what is their purpose?

Thanks for this comment, we have removed all irrelevant definitions.

3)  The fractional order ?<?≤? [in page 4] was not used in the work, so researchers should delete it or give an example that contains it.

Thanks again for your nice observation. We have removed it.

 

4) English requires some improvement.

Improved.

5) Please check each equation, and eliminate some typos.

Corrected 

6) Give an explanation for each figure and what we can conclude from it.

Corrected 

7) If it is possible to include the drawing code in the paper.

I used a simple Mathematica program for graphing. It is not difficult programming.  

8) The convergence of the method must be proven.

Included. 

 

Round 2

Reviewer 1 Report

The revised version of the paper is well improved, I recommend it for publication.