We study a generalized Pólya urn with balls of two colours and a triangular replacement matrix; the urn is not required to be balanced. We prove limit theorems describing the asymptotic distribution of the composition of the urn after a long time. Several different types of asymptotics appear, depending on the ratio of the diagonal elements in the replacement matrix; the limit laws include norm...

We investigate a generalized Langevin equation (GLE) in the presence of an additive noise characterized by the mixture of the usual white noise and an arbitrary one. This scenario lead us to a wide class of diffusive processes, in particular the ones whose noise correlation functions are governed by power laws, exponentials, and Mittag-Leffler functions. The results show the presence of differe...

1050 NOTICES OF THE AMS VOLUME 46, NUMBER 9 T his year marks the thirtieth anniversary of the realization of the dream of one Swedish mathematician. In 1916, on his seventieth birthday, Gösta Mittag-Leffler promised his and his wife’s considerable fortune to the goal of founding a mathematics institute. More than forty years had to pass after his death before the institute was launched in earne...

R.K. SAXENA Department of Mathematics and Statistics, Jai Narain Vyas University Jodhpur 342001, INDIA A.M. MATHAI Department of Mathematics and Statistics, McGill University, 805 Sherbooke Street West, Montreal, CANADA H3A 2K6 H.J. HAUBOLD Office for Outer Space Affairs, United Nations, P.O. Box 500, A-1400 Vienna, AUSTRIA Abstract. The subject of this paper is to derive the solution of genera...

In this paper, the Kharrat–Toma transforms of Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and regularized version HP derivative are derived. Moreover, we also compute solution some Cauchy problems diffusion equations modeled with via transform. The solutions computed in form generalized Mittag–Leffler function.

Abstract This paper addresses the asymptotic behavior of systems described by nonlinear differential equations with two fractional derivatives. Using Mittag–Leffler function, Laplace transform, and generalized Gronwall inequality, a sufficient stability condition is derived for such systems. Numerical examples illustrate theoretical results.

This paper discusses asymptotic behavior of oneand two-parameter PoissonDirichlet models, that is, Ewens models and its two parameter extensions by Pitman, and show that their asymptotic behavior are very different. The paper shows asymptotic properties of a class of oneand twoparameter Poisson-Dirichlet distribution models are drastically different. Convergence behavior is expressed in terms o...