PONE-D-24-46049On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulationsPLOS ONE

Dear Dr. Al-Refai,

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PLOS ONE

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Additional Editor Comments:

According to the reviewers, the article needs major revision to consider it for publication...

Comments from PLOS Editorial Office: We note that one or more reviewers has recommended that you cite specific previously published works. As always, we recommend that you please review and evaluate the requested works to determine whether they are relevant and should be cited. It is not a requirement to cite these works. We appreciate your attention to this request.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Authors examined “Authors examined “On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations.” The paper has potential to be published in this journal after following major revisions.

1.What are basic gaps which are filled in this research study?

2.Governing equation are note referenced. Reference each equation properly?

3.Please show the novelty and research gap at the end of introduction section by raising some questions which are to be addressed?

1.In the introduction references are little in number, increase it by adding more relevant studies.

2.Is it the original or relevant topic to the field, whose gaps remain to be filled?

3.How is this study compared to the previously published? Which issues are addressed in this which are not in the previously?

4.Is the methodology used here is new developed or the extended the previous one? If it is improved, then what are the basic improvements have been carried out?

5.Try to add some more relevant references to enrich the study literature for clear justification.

6.Authors are advised to explain the graph with physical reasoning about the parameters and properties in which the variations are being observed.

7.What is the main question addressed by the research?

8. What does it add to the subject area compared with other published

material?

9.What specific improvements should the authors consider regarding the

methodology? What further controls should be considered?

10.Are the conclusions consistent with the evidence and arguments presented

and do they address the main question posed?. Improve it.

11.What ranges of all parameters should be given? In the caption mention all of the involved pare metric values for which graphs are plotted, it will help to the reader compare the parametric effects for considered values of the parameters.

12.Write the future works in this studies.

Reviewer #2: Review Report

Title: On the Solutions of Fractional Differential Equations with Modified Mittag-Leffler Kernel and Dirac Delta Function: Analytical Results and Numerical Simulations

Overall Assessment

The paper addresses the solutions of fractional differential equations (FDEs) incorporating a modified Mittag-Leffler kernel and the Dirac delta function. This topic is both relevant and timely, as fractional calculus continues to find applications in modeling memory and hereditary effects in various physical systems. The use of the modified Mittag-Leffler kernel and the interplay with the Dirac delta function offer an interesting and novel perspective that could expand the applicability of fractional calculus.

While the manuscript contains valuable contributions, there are areas requiring improvement in terms of clarity, organization, and rigor. Below, I provide detailed comments and suggestions.

1.To enhance the clarity and accessibility of the proposed methodology, I suggest including a flowchart that outlines the key steps of the approach.

2.Highlight how the proposed method handles challenges like singularities or boundary conditions.

3.The manuscript includes only one numerical example, which, while illustrative, limits the depth of validation for the proposed methodology. To strengthen the results and provide a more comprehensive evaluation, I recommend the authors to compare the numerical example with solutions obtained using another established method from the literature, such as finite difference, finite element, or other spectral methods. Highlight the differences in accuracy, convergence rates, and computational efficiency between the proposed method and the chosen benchmark method.

4.The authors should consider citing additional relevant works in the field. Specifically

https://doi.org/10.1088/1402-4896/ac1ccf; https://doi.org/10.1155/2021/6662808; https://doi.org/10.1155/2020/1274251

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Reviewer #1: No

Reviewer #2: No

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On the solutions of fractional differential equations with modified Mittag-Leffler kernel and Dirac Delta function: Analytical results and numerical simulations

PONE-D-24-46049R1

Dear Dr. Al-Refai,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Mahmoud H. DarAssi, Ph.D

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: N/A

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors have revised the manuscript properly by incorporating all of the corrections. Now the article is accepted for publication in its current form.

Reviewer #2: The authors have addressed all the comments raised during the review process. I find the revised manuscript acceptable for publication in its current form.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

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