The main aim of this paper is to introduce generalized forms of operational rules associated with operators corresponding to a generalized Hermite matrix polynomials expansions. The associated generating functions is reformulated within the framework of an operational formalism and the theory of exponential operators. We obtain to unilateral and bilateral generating functions by using the same ...

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

Running head: Exponential Approximation by Stein’s Method Version of 8/16/08 By Sourav Chatterjee, Jason Fulman, and Adrian Röllin Abstract: General Berry-Esséen bounds are developed for the exponential distribution using Stein’s method. As an application, a sharp error term is obtained for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is t...

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...