Erratum to: On the existence of mild solutions to the Cauchy problem for a class of fractional evolution equation

After publication of our work [1] we noticed that there were errors in some equations.

The original equations and corrected equations are given below.

In Remark 2.11 on page 5, ‘at $t=0$.’ should be ‘at $t=0$ when $h(0,x(0))=0$.’

At the end of (3.2) on page 7, ‘=0.’ should be ‘$ds=0$.’

In (1) of Theorem 3.1, on line 14 of page 7, ‘$x_{0}\in D(A^{\beta})$’ should be ‘$x_{0}\in D(A^{\alpha+\beta})$’.

In Step 1 of the proof of Theorem 3.1, on line 2 of page 8,

$$\sup\{\eta(t)\}\leq K $$

should be

$$\sup_{t\in R^{+}} \eta(t)\leq K. $$

In Example 4.2, on page 13, ‘Schro” dinger’ should be ‘Schrödinger’.