Solving a Generalized Fractional Nonlinear Integro-Differential Equations via Modified Sumudu Decomposition Transform

Round 1

Reviewer 1 Report

The work is well written, it is clearly understood which is the author's contribution and which is not. The citations reinforce the foreign ownership of the work. I recommend the paper for publication.

 

Author Response

Dear Professor

Thank you very for your effort in referring the paper. The present version has been modified, there is some improvement over the previous version with regard to language and the addition of some references.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments for author File: Comments.pdf

Author Response

Dear Professor

 

Thank you very for your effort in referring the paper. The below remarks are all correct which have been taken and corrected. The present version has been modified, there is some improvement over the previous version with regard to language and the addition of some references

 

(1) Please check f (k) (0−) in the Lemma 1.

(2) Please change “N ” into “N” in the Definition 3.

(3) Please need to set of index j in the set of functions A in the Definition 4.

On page 6:

• Please change “∑∞ n=0 Ei” into “∑∞ n=0 En” in the Equation (8).
• On page 7:

(1) Please change “∑∞ n=0(Ci)k” and “∑∞ n=0(Di)k” into “∑∞ k=0(Ci)k” “∑∞ k=0(Ci)k” the bottom of in the line 155 and 158.

• On page 14 – 15:

(1) Please unify the format of the References

All above remarks raised by you has been corrected.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

In the paper, an effective method for approximate solving nonlinear integro-differential equations with fractional derivatives, by means Sumudu transform and Adomian’s polynomials is presented. Presentation of the paper is clear. There are some minor comments:

1. In (1) the G_j(v(t)) is not explained.

2. In (3), v^{(\alpha)}(x) is not defined.

3. Line 99: perhaps is better to replace "derivative operator" by "integral operator".

4. In Examples 1 and 3 as independent variable is used "t", but in the previous considerations and in Ex. 1 variable "x" is used. It should be unified.

4. In Examples 1 -- 3 the notation D^\alpha is used but in the text is used v^\alpha. It should be unified.

5. In all figures the axes should be labeled.

Author Response

Thank you very for your effort in referring the paper. The below comments are all correct which have been taken and corrected. The present version has been modified, there is some improvement over the previous version with regard to language and the addition of some references

1. In (1) the G_j(v(t)) is not explained.
2. In (3), v^{(\alpha)}(x) is not defined.
3. Line 99: perhaps is better to replace "derivative operator" by "integral operator".
4. In Examples 1 and 3 as independent variable is used "t", but in the previous considerations and in Ex. 1 variable "x" is used. It should be unified.
5. In Examples 1 -- 3 the notation D^\alpha is used but in the text is used v^\alpha. It should be unified.
6. In all figures the axes should be labeled.

All above comments raised by you has been corrected.

Author Response File: Author Response.pdf