I noticed analog read value is fluctuating when I am trying the analoginoutserial example . I have tried with the external power source as well, but no change in the result. I am seeing +/- 3 fluctuations in the analog read value. I have placed the capacitors across the pot and analog input pin and GND, I can see the fluctuations reduced, but I am still seeing +/- 1. When I placed the DMM across the analog pin and GND on 2000mV range, I can see a voltage fluctuation of +/- 2. Why the voltage is fluctuating? I guess this voltage fluctuation is affecting the analog read value. Is there a way to stop these fluctuations?
No, there isn't. You will always experience fluctuations of one or two counts in analog readings. That is partly because of the way the A/D converter works, and also partly because of the way the pot works.
Because the pot has a moving contact, even when you are not turning it, the contact between the two moving surfaces in the pot is varying at the microscopic level, and this affects the current transmission and the apparent output voltage of the pot.
A measurement = best estimate of the measurement +/- uncertainty (error) in measurement
Uncertainty in a digital measuring device is equal to the smallest increment (always the least significant bit).
If you are powering the Arduino from USB then the biggest source of error may well be fluctuations in the voltage of the +5V supply while the reading is being processed by the ADC. For more accurate results, connect the pot between +3.3V and ground, and also use +3.3V as the analog reference. Read the precautions for using an external analog reference before doing this.