Q:

Persuading people of my usefulness

Although I am more experienced than others in some field (Programming and Electronics, but that's not so relevant to the question), I am never given the opportunity to show my worth. The "people" and "others" I am referring to are friends of mine.
I doubt it is because I constantly say "I am better", because I don't say that. There have also been many occasions where a problem remained unsolved for days, because no one listened when I explained that I can solve it, and also when I explained the solution itself, it was disregarded.
How can I show people that I can be useful, and that asking me for help can be worth the "effort"? 
I am simply not given opportunities to show my usefulness, whilst other people (who have less experience than I do) are constantly asked for help, which they often can't give.

A:

Just do it.
If there is a problem that you can solve easily and your friends cannot. Just solve it. I understand that this might not be possible in some situations, but, if your friends see you effectively solve this one then they will know your skill and ask you in the future.
Talk about it
Another way is to casually bring it up in conversation maybe if someone asks "what are you guys doing this week" or something to that effect you could talk about what you like to do in your spare time / for a living / whenever you do programming and electronics.
If your friends are interested in it, you might be able to go into a bit more detail about your projects / job / whenever you do programming and electronics and they might start asking you for help right then!

A:

There have also been many occasions where a problem remained unsolved for days, because no one listened when I explained that I can solve it, and also when I explained the solution itself, it was disregarded.

I think the best way to prove something to someone is by doing the task at hand, and notifying people/friends later.
Also, don't mind me saying but if the people show the careless attitude like your friends showed, you might consider finding new friends, who if not encourage, at least show an appetite to listen to you and not disregard you totally.

