not including class header when only declaration is exist

I have the following case:

class_a.hpp:

#include "class_b.hpp" // is this "include" mandatory?
class class_a{
private:
    class_b b;
};

class_a.cpp:

#include "class_b.hpp"
//code that uses member variables and functions from class_b 

class_b.hpp:

class class_b{};

Is it possible to get rid of #include "class_b.hpp" in the class_a.hpp? Since it is just decleration, why I can not just use forward declaration and not including it? (I tried but it was not compiled)

Of Course I have included class_b.hpp it in the class_a.cpp.