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The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. 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 caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this 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 applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. 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, control theory and several other related areas.

Mathematical physics. --- Special functions. --- Mathematical models. --- Integral equations. --- Probabilities. --- Mathematical Physics. --- Special Functions. --- Mathematical Modeling and Industrial Mathematics. --- Integral Equations. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Equations, Integral --- Functional equations --- Functional analysis --- Models, Mathematical --- Simulation methods --- Special functions --- Mathematical analysis --- Physical mathematics --- Physics --- Functions, Special.

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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

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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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Algebra --- Probability theory --- Mathematics --- Mathematical physics --- algebra --- waarschijnlijkheidstheorie --- functies (wiskunde) --- mathematische modellen --- wiskunde --- fysica

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"This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory. A unique, comprehensive overview of fractional calculus and its applications. With authoritative contributions from the world's leading experts. Of interest to mathematicians, physicists, and engineers."--Provided by publisher.

Fractional calculus.