Delay in picking speed and changing gears

[zakasate]

I have an automatic transmission Vitz and I am noticing that when i start off there is a delay in the picking up of speed. i checked the fuel filter i couldn't find one, i checked in the tank the mesh filter in the in the fuel pump it is OK. what could be the problem does this have to do with the fuel system or gear changing system? otherwise when it has picked speed everything is OK its just at the beginning