Hi @Ahmed_ELSHAHAWY,
Being that we are in the colder seasons, your grass won't be actively growing, so some browning and die off is to be expected. I wouldn't worry about it too much at this point.
To me, it looks like this is a low spot where water is pooling when it rains. This would explain the browning on either side of the path.
My suggestion, which can be done right now, is to aerate the soil to help with drainage. You can use a garden fork or aerator to poke holes in the soil and gently loosen it. This will help with drainage without stressing your lawn too much. Check out How To Aerate Your Lawn for some guidance.
When the weather warms up and your grass is actively growing, I'd suggest you periodically topdress the area to bring the ground up in line with the concrete path. You'll want to apply a layer of topsoil around 10-15mm thick, then spread and level it with a soil spreader or rake, and then allow the grass to grow through. After a couple of weeks, when the grass has grown through this new soil layer, repeat the process. Keep repeating until the soil is at the same level as the concrete path. This will stop the pooling water from getting trapped in this corner. Check out How To Topdress Your Lawn for further guidance.
Let me know what you think and if you have further questions, please don't hesitate to ask.
Jacob
