The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to khypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

In this paper we analyze the convergence of some commonly used Krylov subspace methods for computing the action of matrix Mittag-Leffler functions. As it is well known, such functions find application in the solution of fractional differential equations. We illustrate the theoretical results by some numerical experiments.

Linear operators which (1) preserve the reality of zeros of polynomials having only real zeros and (2) map stable polynomials into stable polynomials are investigated using recently established results concerning the zeros of certain Fox–Wright functions and generalized Mittag-Leffler functions. The paper includes several open problems and questions.  2005 Elsevier Inc. All rights reserved.

In the paper, an overview is presented of results on convergence rate bounds in limit theorems concerning geometric random sums and their generalizations to mixed Poisson sums, including case where mixing law itself a exponential distribution. The main focus upper for Zolotarev ζ-metric as distance between pre-limit laws. New are that extend existing estimates (in well-known Rényi theorem) cons...

By using a class of aggregation control functions, we introduce the concept multiple-HU-OS1-stability and get an optimum approximation for nonlinear single fractional differential equation (NS-ABC-FDE) with Mittag–Leffler kernel. We apply alternative fixed-point theorem to prove existence unique solution NS-ABC-FDE in symmetric matrix-valued FBS. Finally, example, show application obtained resu...

is a monomorphism for all collections of right R-modules {Ni : i ∈ I} . Restricting the Ni to certain classes of modules one obtains various relativized concepts. For instance, Goodearl investigated this notion relativized to flat modules. The present study provides a uniform background for such relativizations and thus covers and generalizes, among others, a number of known results about such ...