The Griffin Cryer by Julia Hughes

Frankie has more problems than most teenage girls: Her brother’s in a coma; her father has deserted them. School friends can’t possibly understand, so she shuns their attempts to sympathise and becomes a loner.
Then one evening, while walking her brother’s dog over the village common, she accidentally summons a griffin – and its rider – from another dimension.
Frankie’s problems are only just beginning.