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Transmutations Singular And Fractional Differential Equations With Applications To Mathematical Physics

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Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics

Transmutations  Singular and Fractional Differential Equations with Applications to Mathematical Physics Book
Author : Elina Shishkina,Sergei Sitnik
Publisher : Academic Press
Release : 2020-07-24
ISBN : 0128204079
Language : En, Es, Fr & De

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Book Description :

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details Enables researchers, lecturers and students to find material under the single "roof"

Direct and Inverse Sturm Liouville Problems

Direct and Inverse Sturm Liouville Problems Book
Author : Vladislav V. Kravchenko
Publisher : Springer Nature
Release : 2020-08-29
ISBN : 3030478491
Language : En, Es, Fr & De

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Book Description :

This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Transmutation Operators and Applications

Transmutation Operators and Applications Book
Author : Vladislav V. Kravchenko,Sergei M. Sitnik
Publisher : Springer Nature
Release : 2020-04-11
ISBN : 303035914X
Language : En, Es, Fr & De

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Book Description :

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.

Mittag Leffler Functions Related Topics and Applications

Mittag Leffler Functions  Related Topics and Applications Book
Author : Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei Rogosin
Publisher : Springer Nature
Release : 2020-11-28
ISBN : 3662615509
Language : En, Es, Fr & De

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Book Description :

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.

Catalogue Issue

Catalogue Issue Book
Author : Massachusetts Institute of Technology
Publisher :
Release : 1964
ISBN :
Language : En, Es, Fr & De

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Book Description :

Physics Briefs

Physics Briefs Book
Author : N.A
Publisher :
Release : 1994
ISBN :
Language : En, Es, Fr & De

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Book Description :