Here the final result preview:
30 uF condensator and the resistor marked with blue 100k control the speed of the fading. You can replace the 100 kilo ohm resistor with 100k linear potentiometer so you can adjust the speed any time.
You can make the circuit even simplier by leaving out other of the transistors and those leds that are connected to it. Good for power led pulsing etc.
LM324 is an OP-Amp amplifier. There 4 op amp, and we just use 2 op amp in above circuit diagram. You may use the other 2 op-amp to build another similar circuit. Transistor is BC547 and the led is ultra bright red with 220 ohm resistor in series.