The study of amphibians is called batrachology, while the study of both reptiles and amphibians is called herpetology.
ðə stˈʌdi ʌv æmfˈɪbiənz ɪz kˈɔːld bˌætɹɐkˈɑːlədʒi, wˌaɪl ðə stˈʌdi ʌv bˈoʊθ ɹˈɛptaɪlz ænd æmfˈɪbiənz ɪz kˈɔːld hˌɜːpɪtˈɑːlədʒi.