Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics

Transmutations  Singular and Fractional Differential Equations with Applications to Mathematical Physics
Author: Elina Shishkina,Sergei Sitnik
Publsiher: Academic Press
Total Pages: 592
Release: 2020-07-24
ISBN 10: 0128204079
ISBN 13: 9780128204078
Language: EN, FR, DE, ES & NL

Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics Book Review:

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"

Operator Theory and Harmonic Analysis

Operator Theory and Harmonic Analysis
Author: Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Publsiher: Springer Nature
Total Pages: 584
Release: 2021-09-27
ISBN 10: 3030774937
ISBN 13: 9783030774936
Language: EN, FR, DE, ES & NL

Operator Theory and Harmonic Analysis Book Review:

This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.

Direct and Inverse Sturm Liouville Problems

Direct and Inverse Sturm Liouville Problems
Author: Vladislav V. Kravchenko
Publsiher: Springer Nature
Total Pages: 154
Release: 2020-07-28
ISBN 10: 3030478491
ISBN 13: 9783030478490
Language: EN, FR, DE, ES & NL

Direct and Inverse Sturm Liouville Problems Book Review:

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.

Mittag Leffler Functions Related Topics and Applications

Mittag Leffler Functions  Related Topics and Applications
Author: Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei Rogosin
Publsiher: Springer Nature
Total Pages: 540
Release: 2020-10-27
ISBN 10: 3662615509
ISBN 13: 9783662615508
Language: EN, FR, DE, ES & NL

Mittag Leffler Functions Related Topics and Applications Book Review:

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.

Transmutation Operators and Applications

Transmutation Operators and Applications
Author: Vladislav V. Kravchenko,Sergei M. Sitnik
Publsiher: Springer Nature
Total Pages: 686
Release: 2020-04-11
ISBN 10: 303035914X
ISBN 13: 9783030359140
Language: EN, FR, DE, ES & NL

Transmutation Operators and Applications Book Review:

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.

Theory and Applications of Fractional Differential Equations

Theory and Applications of Fractional Differential Equations
Author: A.A. Kilbas,H. M. Srivastava,J.J. Trujillo
Publsiher: Elsevier
Total Pages: 523
Release: 2006-03-02
ISBN 10: 9780444518323
ISBN 13: 0444518320
Language: EN, FR, DE, ES & NL

Theory and Applications of Fractional Differential Equations Book Review:

This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.

Transmutation Scattering Theory and Special Functions

Transmutation  Scattering Theory and Special Functions
Author: R. Carroll
Publsiher: Elsevier
Total Pages: 456
Release: 2011-08-18
ISBN 10: 9780080871806
ISBN 13: 0080871801
Language: EN, FR, DE, ES & NL

Transmutation Scattering Theory and Special Functions Book Review:

Transmutation, Scattering Theory and Special Functions

Basic Theory

Basic Theory
Author: Anatoly Kochubei,Yuri Luchko
Publsiher: Walter de Gruyter GmbH & Co KG
Total Pages: 489
Release: 2019-02-19
ISBN 10: 3110571625
ISBN 13: 9783110571622
Language: EN, FR, DE, ES & NL

Basic Theory Book Review:

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 first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Fractional Calculus for Hydrology Soil Science and Geomechanics

Fractional Calculus for Hydrology  Soil Science and Geomechanics
Author: Ninghu Su
Publsiher: CRC Press
Total Pages: 340
Release: 2020-11-02
ISBN 10: 1351032402
ISBN 13: 9781351032407
Language: EN, FR, DE, ES & NL

Fractional Calculus for Hydrology Soil Science and Geomechanics Book Review:

This book is an unique integrated treatise, on the concepts of fractional calculus as models with applications in hydrology, soil science and geomechanics. The models are primarily fractional partial differential equations (fPDEs), and in limited cases, fractional differential equations (fDEs). It develops and applies relevant fPDEs and fDEs mainly to water flow and solute transport in porous media and overland, and in some cases, to concurrent flow and energy transfer. It is an integrated resource with theory and applications for those interested in hydrology, hydraulics and fluid mechanics. The self-contained book summaries the fundamentals for porous media and essential mathematics with extensive references supporting the development of the model and applications.

Singular and Degenerate Cauchy Problems

Singular and Degenerate Cauchy Problems
Author: Anonim
Publsiher: Academic Press
Total Pages: 322
Release: 1977-01-13
ISBN 10: 9780080956367
ISBN 13: 008095636X
Language: EN, FR, DE, ES & NL

Singular and Degenerate Cauchy Problems Book Review:

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Mittag Leffler Functions Related Topics and Applications

Mittag Leffler Functions  Related Topics and Applications
Author: Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei V. Rogosin
Publsiher: Springer
Total Pages: 443
Release: 2014-10-16
ISBN 10: 3662439301
ISBN 13: 9783662439302
Language: EN, FR, DE, ES & NL

Mittag Leffler Functions Related Topics and Applications Book Review:

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 for Physical Science and Engineering

Mathematics for Physical Science and Engineering
Author: Frank E. Harris
Publsiher: Academic Press
Total Pages: 944
Release: 2014-05-24
ISBN 10: 0128010495
ISBN 13: 9780128010495
Language: EN, FR, DE, ES & NL

Mathematics for Physical Science and Engineering Book Review:

Mathematics for Physical Science and Engineering is a complete text in mathematics for physical science that includes the use of symbolic computation to illustrate the mathematical concepts and enable the solution of a broader range of practical problems. This book enables professionals to connect their knowledge of mathematics to either or both of the symbolic languages Maple and Mathematica. The book begins by introducing the reader to symbolic computation and how it can be applied to solve a broad range of practical problems. Chapters cover topics that include: infinite series; complex numbers and functions; vectors and matrices; vector analysis; tensor analysis; ordinary differential equations; general vector spaces; Fourier series; partial differential equations; complex variable theory; and probability and statistics. Each important concept is clarified to students through the use of a simple example and often an illustration. This book is an ideal reference for upper level undergraduates in physical chemistry, physics, engineering, and advanced/applied mathematics courses. It will also appeal to graduate physicists, engineers and related specialties seeking to address practical problems in physical science. Clarifies each important concept to students through the use of a simple example and often an illustration Provides quick-reference for students through multiple appendices, including an overview of terms in most commonly used applications (Mathematica, Maple) Shows how symbolic computing enables solving a broad range of practical problems

On a Class of Singular Cauchy Problems

On a Class of Singular Cauchy Problems
Author: Jan Derk Siersma
Publsiher: Unknown
Total Pages: 159
Release: 1979
ISBN 10: 1928374650XXX
ISBN 13: UCAL:B2706520
Language: EN, FR, DE, ES & NL

On a Class of Singular Cauchy Problems Book Review:

Fractional Integrals and Derivatives ldquo True rdquo versus ldquo False rdquo

Fractional Integrals and Derivatives   ldquo True rdquo  versus  ldquo False rdquo
Author: Yuri Luchko
Publsiher: MDPI
Total Pages: 280
Release: 2021-03-16
ISBN 10: 303650494X
ISBN 13: 9783036504940
Language: EN, FR, DE, ES & NL

Fractional Integrals and Derivatives ldquo True rdquo versus ldquo False rdquo Book Review:

This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.

Inequalities for Differential and Integral Equations

Inequalities for Differential and Integral Equations
Author: Anonim
Publsiher: Elsevier
Total Pages: 611
Release: 1997-11-12
ISBN 10: 0080534643
ISBN 13: 9780080534640
Language: EN, FR, DE, ES & NL

Inequalities for Differential and Integral Equations Book Review:

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course. Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books Provides a valuable reference to engineers and graduate students

Zeta and Q Zeta Functions and Associated Series and Integrals

Zeta and Q Zeta Functions and Associated Series and Integrals
Author: H. M. Srivastava,Choi Junesang
Publsiher: Elsevier
Total Pages: 657
Release: 2012
ISBN 10: 0123852188
ISBN 13: 9780123852182
Language: EN, FR, DE, ES & NL

Zeta and Q Zeta Functions and Associated Series and Integrals Book Review:

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions

Direct and Inverse Problems of Mathematical Physics

Direct and Inverse Problems of Mathematical Physics
Author: R.P. Gilbert,Joji Kajiwara,Yongzhi S. Xu
Publsiher: Springer Science & Business Media
Total Pages: 453
Release: 2000-04-30
ISBN 10: 9780792360056
ISBN 13: 0792360052
Language: EN, FR, DE, ES & NL

Direct and Inverse Problems of Mathematical Physics Book Review:

This volume consists of papers presented in the special sessions on "Wave Phenomena and Related Topics", and "Asymptotics and Homogenization" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT -9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the 'participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of the ISAAC Congresses. We decided to include with the papers presented in the ISAAC Congress and the U.S.-Japan Seminar several very good papers by colleagues from the former Soviet Union. These participants in the ISAAC Congress attended at their own expense. This volume has the title Direct and Inverse Problems of Mathematical Physics which consists of the papers on scattering theory, coefficient identification, uniqueness and existence theorems, boundary controllability, wave propagation in stratified media, viscous flows, nonlinear acoustics, Sobolev spaces, singularity theory, pseudo differential operators, and semigroup theory.

Transmutation Operators and Applications

Transmutation Operators and Applications
Author: Vladislav V. Kravchenko,Sergei M. Sitnik
Publsiher: Birkhäuser
Total Pages: 686
Release: 2021-04-12
ISBN 10: 9783030359164
ISBN 13: 3030359166
Language: EN, FR, DE, ES & NL

Transmutation Operators and Applications Book Review:

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.

Mathematical Reviews

Mathematical Reviews
Author: Anonim
Publsiher: Unknown
Total Pages: 135
Release: 2004
ISBN 10: 1928374650XXX
ISBN 13: UVA:X006180633
Language: EN, FR, DE, ES & NL

Mathematical Reviews Book Review:

STAR

STAR
Author: Anonim
Publsiher: Unknown
Total Pages: 135
Release: 1968-11
ISBN 10: 1928374650XXX
ISBN 13: UIUC:30112057077262
Language: EN, FR, DE, ES & NL

STAR Book Review: