how could i achieve to have a brush like the one in the picture with both tips fading? I checked in the brush window but I could only affect (alpha and size) the ending tip of the brush stroke..
You need a graphic Tablet, such as a Wacom Bamboo or Wacom Intuos, in order to achieve those types of strokes.
Without a tablet, you are limited to fading only one end of the brush.
Scotts answer is not exactly true. Yes, you can only fade out the end, if you want to draw freely, but in this case you can replicate this effect without a tablet.
And this is how you do it:
Photoshop simulates the pen pressure as seen in the brush preview window. It starts with a pressure of 0, goes up to 100 and back to 0. All of this in a linear way, following the path. You will not be able to manipulate this behavior, but it is handy for exactly the case, described in the question.