I hope for your sake that isn't garlic mustard I see back there. That stuff will crowd out any 'good' plants and seed like crazy.

Since mowing grass close to fences is a problem most of us that have fences around put some kind of border down and that helps control that unwanted plant growth called "weeds". Depending on what I want I have used a thick mulch, wood planks (2 x 6 inch boards) laid flat, or paving blocks. Mulches need to be replaced and often those "weeds" can grow in the mulch but usually less so than on bare ground. Wood planks can be had that will fit most any place and have no seams that would allow unwanted plant growth, while the paving blocks will have those seams. The seams will require periodic lifting and cleaning of accumulated organic material that can support those unwanted plants.

kimmq is kimmsr

Laying cardboard with leaves on top could last a few years. You could hoe the area, lay down cardboard, put hoed weeds on top then add leaves. If you don't have leaves then it would be a fall project.

My place doesn't back up to any sort of wild space, green space, etc. But we have weeds any way, just as does every one else.

They blow in.

They come in, unseen, with purchased and/or gift plants.

They're carried in on clothing & pets.

You will have them in spite of any sort of barrier/wall you install.

The way to stop them is awareness. Monitor the area and act while they are seedling size. Don't let them get to the flower/seed stage. Walk the line weekly and pull, spray, or use whatever else may be your choice of weapons.

Cardboard, with leaves or most any other mulch material, has never lasted years In my yard, one season at best. A 2 x 6 or a 2 x 8 board however last for a long time unless someone that does not know the purpose of that board picks it up and throws it away.

kimmq is kimmsr