UNLABELLED This paper deals with the study of a generalized function of Mittag-Leffler type. Various properties including usual differentiation and integration, Euler(Beta) transforms, Laplace transforms, Whittaker transforms, generalized hypergeometric series form with their several special cases are obtained and relationship with Wright hypergeometric function and Laguerre polynomials is also...

In this paper, we shall discuss the properties of the well-known Mittag–Leffler function, and consider the existence of solution of the periodic boundary value problem for a fractional differential equation involving a Riemann–Liouville sequential fractional derivative by means of the method of upper and lower solutions and Schauder fixed point theorem.

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.

Abstract In the present paper we introduce some expansions, based on the falling factorials, for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Faá di Bruno formula, Bell polynomials, potential polynomials, Mittag-Leffler polynomials, derivative polynomials and special numbers (Eulerian numbers and Stirling numbers of both kinds). We investigate the rate of con...