Regeneration is the growing back of the lost part of the body of an organisms 
fragmentation is the unintentionally cutting of of the body leaving its tail behind and grow it back later on

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Fragmentation is a process in which a part of an organism is seperated and on cell division grows into new organism.but in regenration the cells develop into a new organism. yhe major difference is that in fragmentation two living beings are formed but in regenaration only one organism develops completly and gains life.e.g:earthworm