Caputo Fractional Evolution Equations in Discrete Sequences Spaces

Round 1

Reviewer 1 Report

The manuscript introduces representation of the fundamental solutions for semi discrete Caputo fractional differential equations.  It uses techniques from Functional Analysis to calculate the explicit solution of the problem.

The results are novel continuation of previous authors' works. The problem is well-described. The representations of its solution are rigorously provided. The proof of the main manuscript's results is, from the best of my understanding, right.

The paper is well organized and well written. The obtained result is new and  essential . In my opinion this paper fully  deserve on publication.
The introduction is in a good writing and has a survey of some previous studies in the literature and the motivation is clear. The results seem to be correct and interested and deserve to publish.  However, the authors have to introduce a conclusion to show what they did and what its importance. Also, there are some typos must check with the punctuation and grammar rules. For example not limited:
P2, L30  Also,  L47 Finally , etc.
P 5, L5 What do you mean by \Phi_\gamma(t)?


 

Author Response

Dear Referee.

We have followed your instruccions in the new version.

(1) We have corrected the misprint that you have indicated and other more.

(2) We have deleted the L5 in P5. In fact, the function $\Phi_\gamma$ does not play any role in the paper.

(3) We have included a new section about conclusions.

Our best regards

The Authors

Reviewer 2 Report

Comments for author File: Comments.pdf

Author Response

Dear Referee

We have followed your instructions and we have included a new section about Conclusions and future research.

Our thanks

The authors