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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.

Mathematics --- Algebra --- Algebraic geometry --- Operational research. Game theory --- Probability theory --- Planning (firm) --- algebra --- waarschijnlijkheidstheorie --- stochastische analyse --- functies (wiskunde) --- mathematische modellen --- wiskunde --- kansrekening

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This book contains survey papers based on the lectures presented at the 3rd International Winter School “Modern Problems of Mathematics and Mechanics” held in January 2010 at the Belarusian State University, Minsk. These lectures are devoted to different problems of modern analysis and its applications. An extended presentation of modern problems of applied analysis will enable the reader to get familiar with new approaches of mostly interdisciplinary character. The results discussed are application oriented and present new insight into applied problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics.

Mathematical analysis. --- Mathematical analysis --- Number theory --- Differential equations --- Functions of complex variables --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Applied Mathematics --- Mathematics. --- Math --- 517.1 Mathematical analysis --- Functions of complex variables. --- Partial differential equations. --- Functions of real variables. --- Number theory. --- Functions of a Complex Variable. --- Partial Differential Equations. --- Number Theory. --- Real Functions. --- Science --- Differential equations, partial. --- Number study --- Numbers, Theory of --- Algebra --- Partial differential equations --- Complex variables --- Elliptic functions --- Functions of real variables --- Real variables

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