Fractional Integral Equations Tell Us How to Impose Initial Values in Fractional Differential Equations

Round 1

Reviewer 1 Report

In this paper, the author concerns with the notion of the initial value problem in the case of fractional differential equations. The results are presented with mathematical rigour. In this way, the author points out inaccuracies in the previous works concerning fractional differential equations.
For this reason, I think that this paper is important and I recommend it for publication.

Author Response

I am very glad that Reviewer #1 finds the contributions of the paper significant, rigorous, well-written and recommends it for publication.

The paper has been now formatted in the journal style.

Reviewer 2 Report

The paper addresses an important problem in fractional calculus: how to impose initial values to fractional differential equations with Riemann-Liouville derivatives, considering the theory of Volterra integral equations of convolution type. The main result of this paper is the determination of the exact number of initial conditions (which is smaller than the ceiling of the order) which have to be imposed to a fractional differential equation with RL derivatives, in order to guarantee the existence of a unique solution. 

The results are presented in a mathematically rigorous way and the explanations are easy to follow and extremely informative. I believe this paper is very well written and I recommend its acceptance. 

Author Response

I am very glad that reviewer #2 finds the contributions of this paper significant, easy to follow, and well written recommending its acceptance.

The paper has been now formatted in the journal style.