My child is scheduled for an operation shortly but the hospital demands the father's consent before operating, but he left Israel years ago,has no family here,and cut off all contact.What can I do?

Apply to the family court for an order obliging the hospital to perform the operation on the basis of your consent alone. You will  need to attach relevant supporting documentation from the hospital as well as a declaration concerning your inability to contact the father and any unsuccessful efforts to do so.