1) Wake On LAN - Sending Magic Packet via SmartPhone:
If your mobile phone is in the same Wi-Fi network as the PC, then its pretty much about downloading any suitable app on your Smartphone. One which I have tried and tested on Android goes by the name of Wake on LAN and its link can be found here. It asks for the IP Address of the PC and the MAC (Physical address) of the NIC and sends the magic packet via Wifi Network.
2) Configuring routers for using Wake on LAN remotely (outside local network)
Although its quite difficult to wake PCs if they are behind corporate firewalls or in protected by certain Anti-Viruses, still with some help from your IT administrator and proper permissions it can be achieved.
Lets discuss the easier part as of now where we will assume that the PC is connected to a simple router with a static / dynamic IP address from the internet. Wake-on-LAN normally uses UDP ports 7 and 9. These ports need to be forwarded to any IP address in the local network. The packets are sent to the special broadcast address of the LAN, so
it will be received by all network-attached hosts, rather than by a
specific host.The MAC address is used to identify the particular host that should "Wake Up". If the PC is Wake-on-LAN enabled it will be listening for packets on the above ports.If the magic packet is coming from the internet (WAN) then any
firewall must be set up to allow entry of the Wake-on-LAN signal to a
specified port, which can be forwarded to the computer to be woken up.Some routers permit the packet to be broadcast to the entire LAN.Some routers do not support this as they will not forward broadcast packets as mentioned previously.
For any queries or suggestions do write back!