I have Compaq presario laptop with Broadcom Corporation BCM4311 802.11b/g wireless adapter. I am using fedora core 10. I am able to connect to wireless routers and browse internet. These types of connections are shown as in infrastructure mode.
The problem arises when I connect to an ad hoc wireless network. I am trying to connect with my phone using ad hoc network to access internet. I can connect and browse for some time but after that the system hangs.

I can browse normally if I connect to a wireless router.

First of all Fedora 10 lacks the required security fixes to be safe on the 'net, it lacks enhancements and it is unsupported. It may be all you have right now but it should not be used. Please install Fedora 14 or move to a distribution with a slower release cycle. When diagnosing wireless problems it's good to start with posting hardware specs and network configuration and acquire baseline data (wireless-tools output you get from being connected to a stable wireless AP) and then log verbosily when connected to your phone so you at least have data to compare.