Make template function to destinguish inheritors and others

I have a class (base) which has many inheritors (derived_i) and some other types (other). I want to have a template method in some class-handler (caller), which handles inheritors of base in differ way, then from other types.

Here is an example code I telling about.

#include <iostream>

using namespace std;

template <typename T>
class base {
public:
    base (T val = T())
        : m_val(val)
    {}
    base (const base &other)
        : base(other.m_val)
    {}
    virtual void base_specific_method()
    {
        cout << __func__ << " method called: " << m_val << endl;
    }
    void each_class_has_this() {
        cout << __func__ << " this is boring..." << endl;
    }
    T m_val;
};
class other {
public:
    void each_class_has_this() {
        cout << __func__ <<" this is boring..." << endl;
    }
};
class derived_i : public base <int>
{
public:
    derived_i () : base <int> (10)
    {}
    virtual void base_speciffic_method()
    {
        cout << __func__ <<" Hey! I'm interesting derived! And 10 == " << m_val << endl;
    }
};

template <typename T>
class caller {
public:
    caller (T val = T())
        : m_val(val)
    {}
    void call() {
        p_call(m_val);
    }
private:
    template <typename T1> void p_call (T1 &val)
    {
        val.each_class_has_this();
    }
    template <typename T1> void p_call (base<T1> &val)
    {
        val.base_specific_method();
    }
private:
    T m_val;
};

int main ()
{
    caller<other> c1;
    caller<base<double> > c2;
    caller<derived_i > c3;

    c1.call();
    c2.call();
    c3.call();
}

It compiled with g++ -std=c++11 test.cpp and output is next:

  each_class_has_this this is boring...
  base_specific_method method called: 0
  each_class_has_this this is boring...

While I'm expecting

  each_class_has_this this is boring...
  base_specific_method method called: 0
  base_specific_method Hey! I'm interesting derived! And 10 == 10

Is there any way to change this code to make it suitable my requests?

P.S. There is no way to make base and other the inheritors from one class. =(