Mittag-Leffler Functions, Related Topics and Applications

R. Gorenflo. In 1960, he received his doctorate in Karlsruhe for work on entire transcendental functions. Starting in 1974 he served as a Professor at the Free University Berlin, where he retired in 1998, remaining an active researcher. Since the 1960s he has been actively interested in fractional integral equations and diffusion problems, leading him to a close collaboration with F. Mainardi and other researchers, focusing on fractional differential equations and related special functions, with a particular emphasis on modeling physical processes. His list of publications comprises more than 170 research articles and two monographs. A.A. Kilbas (1948-2010). Graduated at the Belarusian State University in Minsk in 1971, where he received his PhD and Doctor of Sciences degrees before becoming a Professor. A.A. Kilbas was a world-known scientist whose contributions to the theory of integral equations, fractional integro-differentiation, fractional differential equations, integral transforms and special functions are highly regarded by the mathematical community. He was the author of more than 300 research articles and 6 monographs. F. Mainardi. In 1966 he graduated with a degree in Theoretical Physics from the University of Bologna, where he took an advanced degree and continues to serve as a Professor of Mathematical Physics. He is the author of two books, has served as the editor of several compilations and has produced more than 150 research articles in Applied Mathematics, Continuum Mechanics, Wave Motion, Fractional Calculus and Stochastic Processes. S.V. Rogosin. Graduated from the Belarusian State University in Minsk in 1974, where he later received his PhD. His research interests concern boundary value problems, complex analysis, integral equations and fractional calculus and their applications in continuous media mechanics. He is the author of two books, more than 100 research papers, has been the co-organizer of several international conferences and the editor of various compilations.

Preface.- Introduction.- 1.History of Mittag-Leffler functions.- 2.Classical Mittag-Leffler function.- 3.Mittag-Leffler functions with two or three parameters.- 4.Generalized Mittag-Leffler functions.- 5.Mittag-Leffler functions and solution to fractional order equations.- 6.Applications to deterministic models.- 7.Applications to stochastic models.- Appendices.- A. Euler Gamma and Beta-functions.- B. Entire functions.- C. Integral transforms.- D. Mellin-Barnes integral.- E. Elements of fractional calculus.- F. Higher transcendental functions.- References.