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As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control, and several other related areas.

Fractional calculus. --- Integral transforms. --- Mathematical models. --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus --- Models, Mathematical --- Simulation methods --- Functions, special. --- Integral equations. --- Distribution (Probability theory. --- Special Functions. --- Mathematical Applications in the Physical Sciences. --- Mathematical Modeling and Industrial Mathematics. --- Integral Equations. --- Probability Theory and Stochastic Processes. --- Special functions --- Mathematical analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Equations, Integral --- Functional equations --- Functional analysis --- Special functions. --- Mathematical physics. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Physical mathematics --- Physics