Veeam Backup and Replication can handle the backup of SQL Servers and processing transaction logs. Files you see here in the screenshot below are from my daily backup job that runs 1x a week doing a full backup, doing incremental backups the other six days, and doing transaction logs every sixty minutes.
VSM-Metadata for transaction logs on other backups
VBM-Metadata for transactionlogs on full backup
Vlb-Virtual Log Backup (this is where the magic happens.
Hourly, veeam talks to the server, kicks of a VSS provider on the server to process the transaction logs and back them up, writing to a vlb file. It is pretty much the same internal system SQL backup uses, just kicked off with veeam. Two changes have to take place to make this happen. Veeam needs access to the database, and you need to tell Veeam to use the SQL servers vss provider by making a registry change. The backup should be ran with a service account that has sysadmin access to the SQL server.
This is the registry key you need to change as well:
HKEY_LOCAL_MACHINE\SOFTWARE\Veeam\Veeam Backup and Replication\
*Tested on SQL 2014 and SQL 2016sp1