Hassen Abdulkadir (Professor)Woldeyohannes Eyerusalem2020-12-162023-11-042020-12-162023-11-042019-07-09http://etd.aau.edu.et/handle/123456789/24111In this thesis, we investigate the fractional Bernoulli numbers Ba;m and poly- nomials Ba;m(z) for all positive fractions a = ; 6= 0. We establish several properties of these numbers and polynomials which are analogous to the clas- sical as well as hypergeometric Bernoulli numbers and polynomials. We also develop the higher order fractional Bernoulli numbers B(t) a;m and polynomials B(t) a;m(z) and their connection to other identity.enFractionalBernoulliNumbersPolynomialsThesis