Yes, try the first three things, then the fourth as a last resort:
!). Download WiFi Analyzer. Make sure your home WiFi is not competing on the same channel as another router with a strong signal from a nearby house. Move your WiFi router's channel if necessary to one that is unused, or has a pretty low signal. This may help.
2). Try assigning a Static IP Address to the WiFi connection on the phone to your router.
First, do you know how to log into your router? You have to look for the page that indicates something like, DHCP Server and the start of a static address pool. You'll be choosing a number in that range, typically 192.168.1.100 to .192.168.1.150, but could be different on your router.
Second Forget the WiFi Connection.
Then attempt to add the connection back, but choose Advanced option, and changed from DHCP to Static and enter that address.
3). Attempt a System Cache Wipe.
4). Attempt a Factory Device Reset after backing up important content (you will lose program settings and will have to set things up again).