What to do Gap between Concrete Slap and Fence

[Carlton]

Background 

I have poor eyesight and fine motor skills issues which makes garden care difficult at times 

I previously tried to put down weed matt and river rock in the space between neighbors fence and concrete slab but grass has come though.  I probably didn't install weed matt correctly see below 

What can i do with this space that is easy to maintain.  I really don't want neighbor's grass growing through as i would have to constantly use whipper snipper to keep in maintained

seeking advice what to do with the above space that is easy and not time consuming to maintain 

[MitchellMc]

HI @Carlton,

Even with the weed mat installed correctly, the tenacious runners from the grass next door will likely find a path through. The easiest option I can think of would be to poison the grass that is there and then spray that strip periodically with path weeder. Path weeder sticks around in the soil for up to twelve months and prevents weeds from emerging. It should be enough to keep the grass at bay. 

Once the grass is under the control of the weeder, you can look to improve the area aesthetically if you wish.

Please let me know if you have any questions.

Mitchell