Mainardi, Francesco; Mura, Antonio; Pagnini, Gianni The functions of the Wright type in fractional calculus. (English) Zbl 1216.26004 Cialdea, Alberto (ed.) et al., Proceedings of the 4th workshop on advanced special functions and solutions of PDE’s, Sabaudia, Italy, May 25–27, 2009. On the occasion of Paolo Emilio Ricci’s retirement. Potenza: Università degli Studi della Basilicata, Dipartimento di Matematica (ISBN 978-88-902965-8-1/pbk). Lecture Notes of Seminario Interdisciplinare di Matematica 9, 111-128 (2010). Summary: We provide a survey of the transcendental functions known in the literature as Wright functions. We devote particular attention to two functions of the Wright type, which, in virtue of their role in applications of fractional calculus, we call auxiliary functions. We also discuss their relevance in probability theory showing their connections with Lévy stable distributions. At the end, we add some historical and bibliographical notes.For the entire collection see [Zbl 1207.00050]. Cited in 6 Documents MSC: 26A33 Fractional derivatives and integrals 33E12 Mittag-Leffler functions and generalizations 44A10 Laplace transform 45K05 Integro-partial differential equations 60G52 Stable stochastic processes Keywords:Wright functions; Mittag-Leffler functions; fractional calculus; stable distributions PDFBibTeX XMLCite \textit{F. Mainardi} et al., Lect. Notes Semin. Interdiscip. Mat. 9, 111--128 (2010; Zbl 1216.26004)