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Axioms
Volume 9
Issue 4
10.3390/axioms9040121
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Article
Peer-Review Record

Inverse Problem for a Mixed Type Integro-Differential Equation with Fractional Order Caputo Operators and Spectral Parameters

Axioms 2020, 9(4), 121; https://doi.org/10.3390/axioms9040121
by Tursun K. Yuldashev 1,* and Erkinjon T. Karimov 2
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Axioms 2020, 9(4), 121; https://doi.org/10.3390/axioms9040121
Submission received: 25 September 2020 / Revised: 15 October 2020 / Accepted: 16 October 2020 / Published: 20 October 2020
(This article belongs to the Special Issue Nonlinear Differential Equations and Dynamical Systems: Theory and Applications)

Round 1

Reviewer 1 Report

The paper contains new results in the field of inverse problems for fractional DE. The results are well-presented and of interest to  the scientific community. A little polishment of English of the paper is needed. For instance, the word "denotation" used in several places of the paper is not appropriate in this context. It is not common to use apostrophe in genitive case for non-living things like "system’s solvability", "operator’s orders" in the Abstract.

Author Response

Dear Reviewer! Thank you very much for your kind review to my scientific work. I improved the English in the article abstract. I introduced new literatures 19-22, 42 and described the content of these works. Everywhere "denotation" was corrected for "designation". I ask you to continue to support me!

Reviewer 2 Report

the paper is clear and well written, the absctract is well done.

also the introduction, however to better introduce the concepts of the paper, could be useful to add the following references:

[1] Cesarano C (2019). Generalized special functions in the description of fractional diffusive equations. COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS, vol. 10 , p. 31 -40

[2] ASSANTE D, CESARANO C, FORNARO C, VAZQUEZ L (2015). Higher Order and Fractional Diffusive Equations. JOURNAL OF ENGINEERING SCIENCE AND TECHNOLOGY REVIEW, vol. 8, p. 202-204

[3] G. DATTOLI, CESARANO C, P.E. RICCI, L. VAZQUEZ (2003). Special Polynomials and Fractional Calculus. MATHEMATICAL AND COMPUTER MODELLING, vol. 37, p. 729-733

sections from 2 to 7 are well written and correct.

finally the final section (the conclusions) could be extend to better explain the concepts of the paper and also to present future research. in this case could be also add a reference about the numerical investigation:

[4] Dubey R, Mishra L N, Cesarano C (2019). Multiobjective Fractional Symmetric Duality in Mathematical Programming with (C,Gf)-Invexity Assumptions. AXIOMS, vol. 8, p. 1-11

Author Response

Dear Reviewer! Thank you very much for your kind review to my scientific work. I improved the English in the article abstract. I introduced new literatures 19-22, 42 and described the content of these works. Everywhere "denotation" was corrected for "designation". I ask you to continue to support me!

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