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...

*Correspondence: [email protected] 3Department of Mathematical Sciences, UAE University, Al Ain, United Arab Emirates Full list of author information is available at the end of the article Abstract In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involvin...

Makalah ini membahas solusi sistem persamaan diferensial linier homogen fractional orde α dengan turunan Caputo. Bentuk umum diberikan dalam beberapa teorema dan contoh.Kata Kunci: Persamaan fractional, Caputo, Mittag-Leffler.

In this paper, we derive a number of interesting results concerning subordination and superordination relations for certain analytic functions associated with an extension the Mittag–Leffler function.