Nonlocal Boundary Value Problems for Hilfer Generalized Proportional Fractional Differential Equations

Round 1

Reviewer 1 Report

Comments on “Nonlocal Boundary Value Problems for Hilfer Generalized Proportional Fractional Differential Equations”

In this paper, the author proposed the existence and uniqueness of the solutions for the boundary value problems of Hilfer generalized proportional fractional differential equations with multi-point boundary conditions. Some examples are provided to show the applications of the main results. The paper is interesting and contribution to the analytical aspect is novel. The paper can be considered for publication after minor revision.

1. In this research or in this study.
2. The theoretical analysis is important. However, it is difficult to obtain the analytical solution for general fractional equations which makes this paper more important. However, in the introduction, it is much better to add some description about the numerical method for fractional equations to give a big picture to the readers, such as https://doi.org/10.1007/s00366-022-01601-0; https://doi.org/10.1007/s00366-021-01489-2, just to mention a few.
3. Not all the equations are numbered.
4. The proof of some equations should be moved to the end.

Author Response

Response to Reviewer 1

Author Response File: Author Response.pdf

Reviewer 2 Report

Please see the attached reviewer report.

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 2 

Author Response File: Author Response.pdf

Reviewer 3 Report

REVIEWER’s REPORT

In this paper, the authors investigated the existence and uniqueness of solutions for boundary value problems for Hilfer generalized proportional fractional differential equations with multi-point boundary conditions. Using the standard fixed point theorem technique the main results are proved. Finally, two examples are provided to understand the theory part.

The results are good and interesting. However, some corrections are needed to improve the quality of the manuscript:

1. The authors should clearly state the originality of the work since this paper used already existing techniques.  
2. The contribution of this paper needs to explain in more detail.
3. In order to show the efficiency of the method, the comparison result with the existing method can be provided.
4. The conclusion part should be added with future directions in this field.
5. Grammatical errors exist that should be checked and corrected throughout the paper.   
6. Some typos exist that should be checked and corrected throughout the paper

 Considering the above points, I recommend the paper for a MAJOR revision to the journal FRACTAL FRACT.

Author Response

Response to Reviewer 3

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Dear Editor

The authors carried out all the suggestions raised by me. I am also satisfied with the answers provided by the authors. Hence I recommend this paper may be accepted from your esteemed journal. Thanks

Author Response

Response to Academic Editor

Author Response File: Author Response.pdf