On Some Fractional Pearson Equations

Abstract

Abstract In this paper some fractional analogues of classical Pearson differential equations are explicitly solved. Limit transitions between the solutions are analyzed, providing a generalization of well-known transitions between the beta and gamma, and between the gamma and normal distributions. Finally, quasi-polynomials orthogonal with respect to these fractional analogues of the classical distributions are introduced, and some conjectures about their zeros are posed.