Designing a fragmentation database?
Compare a fragmented distributed database with a replicated distributed database.  A replicated database would contain all columns and all records on more than one database instance; whereas, the separate instances of a fragmented distributed database do not all contain the same columns and/or records.

Vertical Fragmentation:
A vertically-fragmented distributed database would consist of separate instances which do not share all columns / attributes.  For example, the database for the sales department might have a column for a customer's interests; however, the database in the accounting department would not need this column.

Horizontal Fragmentation:
A horizontally-fragmented distributed database would exist when separate database instances have a similar schema but contain different types of records.  For example, a company with two locations East and West might have two similar databases; however, the one instance would only contain customers in the East, the other only customers in the West.