How can I explain to people I am not angry or upset with them to a greater extent than anyone else, but rather I just experience my emotions more intensely than others.

I can relate to that feeling. Generally, I wait till I've simmered down a bit and am better able to put my feelings into words. Then I use the metaphor of a rollercoaster -- some people feel things like this ~~~ while others feel them like this /\/\/\/\ and I'm one of the latter.

Explain just as you did now.."I am not angry or upset with you, I just experience my emotions more intensely than others" People are more understanding than you would imagine.

I think you explain it very well in your question: "I just experience my emotions more intensely than others." If this explanation does not help them understand, then I'd say that is their issue, not yours. It's okay to experience your emotions more intensely than others.

By supporting them and telling them that i understand what they are going through. Also by asking them how to sort out their feelings

We are our own best freinds, knowing our own self completely means to know this world and this is the parh which can lead us to understand this world and to know others and also to express ourselves better to others!

Well since you experience you emotions more intensely then maybe you can show them that you are not angry or upset by talking to them. You could talk about things that could maybe make them laugh or they will feel better. Its easier to talk to people, they understand you better that way.

By explaining it calmly. If you try to explain in a state before you calm down, chances are people just won't believe you even if you're telling the 100% truth. Those who really know you will understand that's it's a result of your emotions, not that you're angrier at certain people.

Tell them that you are a passionate person. When you are happy, you are ecstatic but when you are sad, you are melancholy and life seems to look a little more gray. Don't be upset if this is you! :) Just tell people that you feel emotions strongly. This doesn't make you weak or a child, it makes you unique. Many artists possess this quality; look at music for example, if musicians were people who feel emotions on a shallow level, the music of today, and even classical music, would sound so differently. Think of Farrell's "Happy" or Beethoven's "Ode to Joy", feeling intense emotions is just a natural part of life for some people.

This will always be a hard one, people tend not to understand that emotions felt by each person, and its intensities, often depend on the person. The best way to combat this, is to, after reacting in a way you later perceive to be an overreaction, simply explain entirely and apologise. If this person is truly understanding, they will see past it, and will become accustomed to it. I myself have friends who have this problem, but it has never stinted our friendship. Good luck!