New Exact Solutions of Some Important Nonlinear Fractional Partial Differential Equations with Beta Derivative
Round 1
Reviewer 1 Report
In this work, the F-expansion method is used to find exact solutions of the space-time-fractional modified Benjamin Bona Mahony equation and the nonlinear time-fractional Schrödinger equation with beta derivative. One of the most efficient and significant methods for obtaining new exact solutions to nonlinear equations is this method. With the aid of Maple, more exact solutions defined by the Jacobi elliptic function are obtained. Hyperbolic function solutions and some exact solutions expressed by trigonometric functions are gained in the case of m modulus 1 and 0 limits of the Jacobi elliptic function.
This paper is well written in English, but, I have some suggestions as following:
1. Add some details in the section Results and Discussion.
2. Why does the author consider this model? What are the real applications for this model?
3. The introduction should be enhanced.
4. Please, do not use together "time fractional". Please, only use
"time conformable ". Delete fractional words from all the paper.
5. The authors should rearrange their references list.
Author Response
Response to Reviewer 1 Comments
- Add some details in the section Results and Discussion.
Answer : Some necessary details have been added in the section results and discussion.
Why does the author consider this model? What are the real applications for this model?
Answer: The F-expansion approach was an effective, dependable, and strong tool for discovering new precise solutions. When comparing the outcomes of this procedure to earlier publications, it is evident that they are unique. The results suggest that the proposed methods are highly successful, promising, and appropriate for solving other nonlinear fractional differential equations. I believe the findings of this study will be significant in determining the significance of certain linked physical problems.
- The introduction should be enhanced.
Answer : The introduction has been enriched with some additions (such as new citations).
Please, do not use together "time fractional". Please, only use "time conformable ". Delete fractional words from all the paper.
Answer :
Atangana et al. introduced beta derivative as an enlarged version of conformable derivative, as we described in the introduction section of our study. As a result of the research, it was discovered that this derivative satisfies a number of features that are considered a limitation for fractional derivatives and are used to represent a variety of physical problems. Furthermore, the fact that it is a natural extension of the classical derivative has been eliminated the impossibilities in other derivatives, despite the fact that it is not considered a fractional derivative.
In this study, two fractional equations that exist in the literature are discussed. Especially since they are time-fractional equations, the transformation equations used are designed according to this situation and the solutions of these equations are built on this situation. For this reason, the word "fractional" is important for the integrity of the study. This word has always been used in all previous studies for the solutions of fractional differential equations. In this study, differential equations in the form of both space-time and time fractional are discussed.
The above notations have been accepted and in common in the literature of such studies.
The authors should rearrange their references list.
Answer : The reference list has been prepared in accordance with the journal's writing standards.
Reviewer 2 Report
The considered paper contains very interested results about the fractional calculus
Author Response
Dear Reviewer,
Thank you for your good assessment.
Reviewer 3 Report
The F-expansion method is used to find exact solutions of the space time fractional modified Benjamin Bona Mahony equation and the nonlinear time fractional Schrödinger equation with beta derivative. One of the most efficient and significant methods for
obtaining new exact solutions to nonlinear equations is this method. With the aid of Maple, more exact solutions defined by the Jacobi elliptic function are obtained. Hyperbolic function solutions and some exact solutions expressed by trigonometric functions are gained in the case
of m modulus 1 and 0 limits of the Jacobi elliptic function.
What about using other methods and compare them
Also instead of maple what about the other software like mathematica or mat lab
Author Response
Response to Reviewer 3 Comments
- What about using other methods and compare them
Answer:
We believe that we have reached new results of two important equations with the method we used in this study. So, original results have been obtained. Our aim is to support related studies by our new results in the literature, and to show the effectiveness of the method. In addition to this, we have included the comparison of the results we found with the results previously made using different methods in the conclusion section.
- Also instead of maple what about the other software like Mathematica or mat lab.
Answer:
Our University does not support Mathematica and MATLAB. I have the license of Maple, and I am confident with this software. I am sure almost the same results can be obtained by the softwares Mathematica and MATLAB.
Author Response File: 
Author Response.pdf
Round 2
Reviewer 3 Report
The authors did what was required from them and their answers are clear
