In the first part of the paper, the authors study the existence of a unique solution of the problem
where (HA): is a bounded linear operator on a Banach space for each . The function is continuous in the uniform operator topology. They claim that problem (1) is equivalent to the integral equation
Unfortunately, this claim is not true. This is due to the fact that, since the derivative of in (2), does not exist, consequently, the fractional order derivative does not exist.
So, there is no solution for problem (1).
The second part contains the same error for the nonlinear case of (1).