# 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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:**