How can I write to x-axis what I want please? I would like to write c_0 to the position of 100, c_0/2 to the position of 50 and c_0/4 to the position of 25. Thank you.
Take a look at the documentation, for example by typing help xtics list into gnuplot. For your specific case, try
set xtics ("c_0" 100, "c_0/2" 50, "c_0/4" 25)