There would have been possibility to recover everything the first time your update failed.
Now that the iPhone has been formatted there is absolutely no way to recover any data from your iPhone itself. The data was encrypted and the key is lost. Even if some method allowed you to extract bits and pieces of data from the iPhone, there is no way you could decrypt them.
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Now for the possible: like @refectio (Minho) said, you may have data stored in a recent (or not so recent) back on iCloud or on your/any laptop you previously synced with.
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Now for the possible: like @refectio (Minho) said, you may have data stored in a recent (or not so recent) back-up on iCloud or on your/any laptop you previously synced with.
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You can use iExplorer or similar applications to explore your computer looking for a back-up and can extract your data from it. It can also check your iCloud account for the same.
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You can use iExplorer or similar applications to explore your computer looking for a back-up and can extract your data from it. Some applications like Wondershare can also check your iCloud account for the same.
Manually, you can go to iCloud.com, sign in with your Apple ID and password and see if any of your photos appear there (that's different from a full back-up that could be there as well).
You can also start iTunes, click on "iTunes>Preferences>Devices" and see if you have a back-up listed there.
Let me give you closure:
There would have been possibility to recover everything the first time your update failed.
Now that the iPhone has been formatted there is absolutely no way to recover any data from your iPhone itself. The data was encrypted and the key is lost. Even if some method allowed you to extract bits and pieces of data from the iPhone, there is no way you could decrypt them.
Now for the possible: like @refectio (Minho) said, you may have data stored in a recent (or not so recent) back on iCloud or on your/any laptop you previously synced with.
You can use iExplorer or similar applications to explore your computer looking for a back-up and can extract your data from it. It can also check your iCloud account for the same.
Manually, you can go to iCloud.com, sign in with your Apple ID and password and see if any of your photos appear there (that's different from a full back-up that could be there as well).
You can also start iTunes, click on "iTunes>Preferences>Devices" and see if you have a back-up listed there.
Good luck!