Abstract We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue a different way. Inter-event times all are Mittag-Leffler distributed, which is heavy tail distribution with no moments. For of we answer question being at zero infinitely often (the ‘recurrence’ regime) or not transient regime). Aside from this question, analytical propertie...

Since Gösta Magus Mittag-Leffler introduced the so-called function in 1903 and studied its features five subsequent notes, passing first half of 20th century during which majority scientists remained almost unaware function, various extensions (referred to as type functions) have been researched applied a wide range problems physics, biology, chemistry, engineering. In context fractional calcul...

Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented a closed form. In most reported cases, these new integral expressed as generalized hypergeometric functions, but also terms elementary special functions. Behaviour som...

In this paper, we use the Mittag-Leffler addition formula to solve Green function of generalized time fractional diffusion equation in whole plane and prove convergence function.

In the paper, the authors generalize the notion “k-Mittag-Leffler function”, establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function. 1. Preliminaries Throughout this paper, let C, R, R0 , R, Z − 0 , and N denote respectively the sets of com...