Fasting, in its most simple definition, is going without food. (I've included abstaining from other activities for a particular period of time also as I've found that there are some areas that, at times, also need to be brought under subjection)
And he was three days without sight, and neither did eat nor drink. Acts 9:9
The partial fast is when the diet is restricted.
I ate no pleasant bread, neither came flesh nor wine in my mouth, neither did I anoint myself at all, till three whole weeks were fulfilled. Daniel 10:3
Blow the trumpet in Zion, sanctify a fast, call a solemn assembly. (Joel 2:15)
Fasting does not change God. It changes us. God relates to us on the basis of our relationship with Him. When we change, then the way God deals with us is affected. But fasting does change how He deals with us. The book of Jonah is an example of how this happened in the city of Ninevah.