so how to get rid of plants without using roundup

so along the edge of my property i have these damn tree weeds. i call them this because they crow several feet in a year and sprout up anywhere. there easy to get rid of if you find them early enough.
but my problem is along the property line, this area there quiet well established and id like to get rid of them and plant fruit trees all along this area.
how can i kill them all off without using roundup or anything similar.

I'm wondering what exactly your "weeds" are?  Sort of resemble the white poplar saplings that are a nuisance here but also remind me of Rose of Sharon which can be persistent too.

My advice is labor-intensive I'm afraid.  I'd dig out as many of them as I could, getting as much root as possible if you're planning to plant soon.  If you have a season or two, I'd recommend smothering the area with a thick layer of wood mulch in hopes of discouraging any more from sprouting.  Either way, you will need to be vigilant and pull or grub out sprouts as they appear.

Edit:  I wasn't clear above, but I'd grub out the roots either way.  

looks like ailanthus or sumac. they’re going to be tough to kill with just heavy mulching. solarizing, maybe? get them all cut down to ground level and cover with thick black plastic (or clear, you’re going for a ground level greenhouse effect).

What do the leaves look like?  Are they not pretty in the fall?

To me, they look like they were planted, maybe by a previous owner? Maybe to block pollution from the road?

Have you tried making tea from Black Walnut leaves?

Or maybe try 10% vinegar, it is the kind used for pickling as 5% vinegar will not work.

I'm afraid I don't have an easy answer to your question. When I first bought my property I had patches of 2 different kinds of 'weed trees' around my yard. It might help you to first identify the tree (you can send a picture to your local extension agent and ask for advice)  and then google "how to eradicate (your tree) in your specific area.

In my case I had the Siberian Elm tree which is moderately invasive. And I had one that looked just like your trees in winter. It was the horribly invasive Chinese Tree of Heaven. When I googled 'how to kill it in Arizona I quickly found the website of our local forestry management office which has been battling this tree. It has been wiping out thousands of acres of our native vegetation for years now. And Roundup won't kill it.  

Turns out it's super invasive because (A) it sends out tens of thousands of winged seeds every summer. (B) It sends out runners 20-30 feet long and pops up everywhere. And (C) The runner roots put out a chemical that is seriously toxic to other vegetation. I had to do the same thing that the forest service has been doing, dig up the roots. Luckily, it doesn't have huge tap roots, mostly the runners which were only a foot or so deep so ... it took quite a bit of time and labor but wasn't so very hard to do and it was so worth it.

I hope you find an easier answer. I will definitely be watching this thread for one.

Since I've never considered toxic stuff to be an option it would never be an 'either/or' situation for me...and by having it off the table altogether we don't have to think of it as a 'last resort'  

I think I would start with identifying that sprout  and then probably cut low to the ground and only dig it out where I intended to plant the fruit trees.  

So much would depend on what it is.

That looks like a lovely spot along a railroad...is it still used? could it be that they use some kind of chemicals on the railroad right of way? Is that a walking path next to it?

Is it possible that last owner planted those deliberately for some reason as someone else mentioned above? to prevent chemical drift?

The saplings look large now, but once cut maybe the newly sprouted ones would be maintainable with a good scythe blade and over time that should kill most stemy sprouts.
It looks like it might be too rough to mow with a push mower but if it was smooth enough that would work too...we've kept things at bay by just cutting to the ground and keeping the area mowed.

This is the tree the seeds come from. my wife would love me to cut it down but i like it.

Judith, its a bike/walking path that the opened up a few years ago (maybe 4 or 5 )

at the moment it runs between Bellefontaine Ohio to Springfield Ohio.

in the next year or two it should run into Cincinnati to the south and Toledo to the north. ans of course there are branches to other places i think