Cool Functional Equation

Algebra Level 3

$\large{f(f(x)) = f(x) + x}$

Let $f : \mathbb{R} \to \mathbb{R}$ be a continuous function such that the above equation is satisfied for all $x \in \mathbb{R}$ , and for all $x > 0$ , we have $f(x) > 0.$

If $f(1)=2014,$ find $f(2015).$

Cool Functional Equation

This is a original problem.