Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics

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"

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  • Author : Elina Shishkina
  • Publisher : Academic Press
  • Pages : 592 pages
  • ISBN : 0128204079
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKTransmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics

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
  • Publisher : Academic Press
  • Release : 24 July 2020
GET THIS BOOKTransmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

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

Direct and Inverse Sturm-Liouville Problems

Direct and Inverse Sturm-Liouville Problems
  • Author : Vladislav V. Kravchenko
  • Publisher : Springer Nature
  • Release : 29 August 2020
GET THIS BOOKDirect and Inverse Sturm-Liouville Problems

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

Operator Theory and Harmonic Analysis

Operator Theory and Harmonic Analysis
  • Author : Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
  • Publisher : Springer Nature
  • Release : 27 September 2021
GET THIS BOOKOperator Theory and Harmonic Analysis

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

Mittag-Leffler Functions, Related Topics and Applications

Mittag-Leffler Functions, Related Topics and Applications
  • Author : Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei Rogosin
  • Publisher : Springer Nature
  • Release : 28 November 2020
GET THIS BOOKMittag-Leffler Functions, Related Topics and Applications

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 for Hydrology, Soil Science and Geomechanics

Fractional Calculus for Hydrology, Soil Science and Geomechanics
  • Author : Ninghu Su
  • Publisher : CRC Press
  • Release : 02 November 2020
GET THIS BOOKFractional Calculus for Hydrology, Soil Science and Geomechanics

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

Transmutation Operators and Applications

Transmutation Operators and Applications
  • Author : Vladislav V. Kravchenko,Sergei M. Sitnik
  • Publisher : Springer Nature
  • Release : 11 April 2020
GET THIS BOOKTransmutation Operators and Applications

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

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology
  • Author : Abdon Atangana
  • Publisher : Academic Press
  • Release : 19 September 2017
GET THIS BOOKFractional Operators with Constant and Variable Order with Application to Geo-hydrology

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author’s analyses, the book proposes new techniques for groundwater remediation,

Mathematics for Physical Science and Engineering

Mathematics for Physical Science and Engineering
  • Author : Frank E. Harris
  • Publisher : Academic Press
  • Release : 24 May 2014
GET THIS BOOKMathematics for Physical Science and Engineering

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

Operator Theory, Pseudo-Differential Equations, and Mathematical Physics

Operator Theory, Pseudo-Differential Equations, and Mathematical Physics
  • Author : Yuri I. Karlovich,Luigi Rodino,Bernd Silbermann,Ilya M. Spitkovsky
  • Publisher : Springer Science & Business Media
  • Release : 30 October 2012
GET THIS BOOKOperator Theory, Pseudo-Differential Equations, and Mathematical Physics

This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written

Basic Theory

Basic Theory
  • Author : Anatoly Kochubei,Yuri Luchko
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 19 February 2019
GET THIS BOOKBasic Theory

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.

Derivative with a New Parameter

Derivative with a New Parameter
  • Author : Abdon Atangana
  • Publisher : Academic Press
  • Release : 18 September 2015
GET THIS BOOKDerivative with a New Parameter

Derivative with a New Parameter: Theory, Methods and Applications discusses the first application of the local derivative that was done by Newton for general physics, and later for other areas of the sciences. The book starts off by giving a history of derivatives, from Newton to Caputo. It then goes on to introduce the new parameters for the local derivative, including its definition and properties. Additional topics define beta-Laplace transforms, beta-Sumudu transforms, and beta-Fourier transforms, including their properties, and then

Direct and Inverse Problems of Mathematical Physics

Direct and Inverse Problems of Mathematical Physics
  • Author : R.P. Gilbert,Joji Kajiwara,Yongzhi S. Xu
  • Publisher : Springer Science & Business Media
  • Release : 30 April 2000
GET THIS BOOKDirect and Inverse Problems of Mathematical Physics

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

The Hypergeometric Approach to Integral Transforms and Convolutions

The Hypergeometric Approach to Integral Transforms and Convolutions
  • Author : S.B. Yakubovich,Yury Luchko
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKThe Hypergeometric Approach to Integral Transforms and Convolutions

The aim of this book is to develop a new approach which we called the hyper geometric one to the theory of various integral transforms, convolutions, and their applications to solutions of integro-differential equations, operational calculus, and evaluation of integrals. We hope that this simple approach, which will be explained below, allows students, post graduates in mathematics, physicists and technicians, and serious mathematicians and researchers to find in this book new interesting results in the theory of integral transforms, special

The Swings of Science

The Swings of Science
  • Author : Len Pismen
  • Publisher : Springer
  • Release : 06 December 2018
GET THIS BOOKThe Swings of Science

This book is a personal account of some aspects of the emergence of modern science, mostly from the viewpoint of those branches of physics which provided the much needed paradigm shift of "more is different" that heralded the advent of complexity science as an antidote to the purely reductionist approach in fundamental physics. It is also about the humans that have helped to shape these developments, including personal reminiscences and the realization that the so-called exact sciences are inevitably also