Numerical Treatment of Hybrid Fuzzy Differential Equations Subject to Trapezoidal and Triangular Fuzzy Initial Conditions Using Picard’s and the General Linear Method

Round 1

Reviewer 1 Report

The content of the submitted manuscript is good but the presentation way of current form is not fulfilling the journal requirements. Modification is needed to consider for publication.

  - Title of the paper

The title of the paper looks good but in the same time, it can be modified to represent the manuscript in a better way.

Abstract

-          The abstract is not well written

-          You should include some of the main finding in the abstract section.

Abstract should have a conclusion of the study.

Introduction  

-                 The objective of the study is also not clearly mention.

·       Add more on the basic of the problem in the introduction

·       More details about identified problems are required in the introduction section.

·       The author should focus mainly on the importance and significance of the study.

·       I suggest the author to demonstrate what does the paper add to the current literature? and what new knowledge is added by this study?

Add the unique of this study compared to other studies discuss the same issue.

-Discus merits and limitations of technique applied.

 

 Material and Methods

 

-     The material and method section is too weak in the manuscript and you need to focus on it more.

 

Result and discussion

-                 The presentation fails to discuss the summary, and trying to some of vague reason which is not the explanation.

-                 The explanation for the critical analysis is not sufficient, although some of the good points have has been identified.

 

Conclusion

-          Please rewrite the conclusion with the proper explanation in the R & D.

 

 

Author Response

I would like to thank the respected reviewers for their valuable comments and
suggestions.
We went through the whole paper and tried our best to eliminate any grammatical
or stylistic errors.
The following are the changes that were made to the paper as per the comments of
the referees (please note that the line numbers are as per the downloaded copy
from the Journal not the revised version):
1. Title Modified.
2. Abstract: Rewritten.
3. Introduction: Modified and some of the major modifications are as follows:
- Lines 10-11: most of the two lines omitted.
- After line 36: A full paragraph was added.
- Some references are added after lines 39 and 43.
- Lines 44-49: replaced by new paragraph.
4. Material and methods: some modifications were as follows:
After line 186 and before Subsection 4.2.2: Two short paragraphs in
addition to 4 tables were added for comparison purposes with the results
of applying other methods reported in the literature.
5. Conclusions: The lower half of the conclusion section was rewritten.
6. References:
- The references 5, 6, 17, 20, 21, 27, 28, 29 (old version) were removed.
- The following references were added:
G.Gumaha, M.Nasera, M.Al-Smadib, S..Al-Omaria and D.Baleanuc
(2020) Numerical solutions of hybrid fuzzy differential equations in a
Hilbert space, Appl. Numer. Math. 151, 402–412
E. Hajilou , M. Paripour and H. Heidaria ( 2015), Application of
Differential Transform Method to Solve Hybrid Fuzzy Differential
Equations, Inter.J. Math. Modelling Comput. 05, 203- 217
M. Thangamuthu and J. Thippan (2019) , Numerical Solution for
HybridFuzzy Differential Equation by Fifth Order Runge-Kutta Nystrom
Method, J. Math. Sci. Modelling, 2, 39-50

Author Response File: Author Response.pdf

Reviewer 2 Report

Obviously, I will recommend this paper for publication. Still, I have to share with its authors my concerns. Fuzzy differential equations are at best work in progress and that paper contributes to it. But some aspects of what that paper wants to show are a bit mysterious: the parameter alpha for example is introduced, without introduction and plays a fundamental role in the analysis (look at figure 8 and 9). In my view, fuzzy differential equations have the potential to make a big difference. This is I think the inspiration of that paper. It should be encouraged. So, I strongly recommend its publication.

Author Response

Thanks for the encouraging comments. We went through the paper again and some modifications were done to the paper.

Reviewer 3 Report

• The title and the abstract coincide with the content of the paper. Keywords are well-chosen.
• The problem and goal of the paper are clearly and correctly formulated.
• The manuscript is clear, relevant for the field and presented in a well-structured manner.
• To achieve the goal of the paper, the applied research methods can be considered correct.
• The paper contains a comprehensive reference list. The literature studies presented should be considered sufficient both as to the proper selection of sources and their quantity. The cited references are current.

• In conclusion, I propose

-evaluate the critical research, show its limitations and weaknesses,
- highlight the new knowledge and the lessons learned from it,
- describe the importance of the research and how it affects the wider field, show how the information obtained can be further used

Conclusions must be clearly and unambiguously linked to the results of the survey. Their theoretical and practical implications should be indicated 

Author Response

Thanks for the valuable comments. See the attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Accept