The present chapter discusses new advances in the development of analytical solutions for the fractional version of the Bateman equations, where classical methods used to solve the integer case are extended to the fractional one, using an adequate change of variable. Such task is carried out by observing symmetry in the mathematical expressions, as well as a generalization of partial fraction decomposition theory, where polynomials with fractional orders are considered. Laplace transform, power series method and some relationships related to the 2-parameter Mittag-Leffler function are also analyzed in the present chapter.