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

Elina Shishkina,Sergei Sitnik
Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics Book PDF

Author : Elina Shishkina,Sergei Sitnik
Publisher : Academic Press
Page : 594 pages
File Size : 54,5 Mb
Release : 2020-07-24
Category : Mathematics
ISBN : 9780128204078

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Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics by Elina Shishkina,Sergei Sitnik Pdf

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"

Fractional Differential Equations

Mouffak Benchohra,Soufyane Bouriah,Abdelkrim Salim,Yong Zhou
Fractional Differential Equations Book PDF

Author : Mouffak Benchohra,Soufyane Bouriah,Abdelkrim Salim,Yong Zhou
Publisher : Walter de Gruyter GmbH & Co KG
Page : 336 pages
File Size : 43,9 Mb
Release : 2023-11-20
Category : Technology & Engineering
ISBN : 9783111334387

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Fractional Differential Equations by Mouffak Benchohra,Soufyane Bouriah,Abdelkrim Salim,Yong Zhou Pdf

This book is devoted to the existence and uniqueness results for various classes of problems with periodic conditions. All of the problems in this book deal with fractional differential equations and some fractional derivatives such as the Riemann-Liouville, Caputo and Hilfer fractional derivatives. Classical fixed point theorems as well as the coincidence degree theory of Mawhin are employed as tools.

Transmutation Operators and Applications

Vladislav V. Kravchenko,Sergei M. Sitnik
Transmutation Operators and Applications Book PDF

Author : Vladislav V. Kravchenko,Sergei M. Sitnik
Publisher : Springer Nature
Page : 685 pages
File Size : 49,6 Mb
Release : 2020-04-11
Category : Mathematics
ISBN : 9783030359140

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Transmutation Operators and Applications by Vladislav V. Kravchenko,Sergei M. Sitnik Pdf

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.

Methods of Mathematical Physics

Alexey N. Karapetyants,Vladislav V. Kravchenko
Methods of Mathematical Physics Book PDF

Author : Alexey N. Karapetyants,Vladislav V. Kravchenko
Publisher : Springer Nature
Page : 406 pages
File Size : 55,9 Mb
Release : 2022-11-17
Category : Science
ISBN : 9783031178450

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Methods of Mathematical Physics by Alexey N. Karapetyants,Vladislav V. Kravchenko Pdf

This textbook provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments. Readers will be introduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in textbooks, this will be an ideal text for both introductory and more specialized courses. The first five chapters present standard material, including the classification of PDEs, an introduction to boundary value and initial value problems, and an introduction to the Fourier method of separation of variables. More advanced material and specialized treatments follow, including practical methods for solving direct and inverse Sturm-Liouville problems; the theory of parabolic equations, harmonic functions, potential theory, integral equations and the method of non-orthogonal series. Methods of Mathematical Physics is ideal for undergraduate students and can serve as a textbook for a regular course in equations of mathematical physics as well as for more advanced courses on selected topics.

Differential Equations, Mathematical Modeling and Computational Algorithms

Vladimir Vasilyev
Differential Equations Mathematical Modeling and Computational Algorithms Book PDF

Author : Vladimir Vasilyev
Publisher : Springer Nature
Page : 294 pages
File Size : 47,6 Mb
Release : 2023-06-06
Category : Mathematics
ISBN : 9783031285059

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Differential Equations, Mathematical Modeling and Computational Algorithms by Vladimir Vasilyev Pdf

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Operator Theory and Harmonic Analysis

Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Operator Theory and Harmonic Analysis Book PDF

Author : Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Publisher : Springer Nature
Page : 585 pages
File Size : 40,7 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030774936

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Operator Theory and Harmonic Analysis by Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek Pdf

This volume is part of the collaboration agreement between Springer and the ISAAC society. 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

Vladislav V. Kravchenko
Direct and Inverse Sturm Liouville Problems Book PDF

Author : Vladislav V. Kravchenko
Publisher : Springer Nature
Page : 155 pages
File Size : 51,9 Mb
Release : 2020-07-28
Category : Mathematics
ISBN : 9783030478490

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Direct and Inverse Sturm-Liouville Problems by Vladislav V. Kravchenko Pdf

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.

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems

Yeliz Karaca,Dumitru Baleanu,Yu-Dong Zhang,Osvaldo Gervasi,Majaz Moonis
Multi Chaos Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems Book PDF

Author : Yeliz Karaca,Dumitru Baleanu,Yu-Dong Zhang,Osvaldo Gervasi,Majaz Moonis
Publisher : Academic Press
Page : 352 pages
File Size : 43,8 Mb
Release : 2022-06-22
Category : Science
ISBN : 9780323886161

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Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems by Yeliz Karaca,Dumitru Baleanu,Yu-Dong Zhang,Osvaldo Gervasi,Majaz Moonis Pdf

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou
Fractional Differential Equations And Inclusions Classical And Advanced Topics Book PDF

Author : Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou
Publisher : World Scientific
Page : 326 pages
File Size : 49,7 Mb
Release : 2023-02-02
Category : Mathematics
ISBN : 9789811261275

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Fractional Differential Equations And Inclusions: Classical And Advanced Topics by Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou Pdf

This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.

Generalized Fractional Calculus and Applications

Virginia S Kiryakova
Generalized Fractional Calculus and Applications Book PDF

Author : Virginia S Kiryakova
Publisher : CRC Press
Page : 412 pages
File Size : 53,8 Mb
Release : 1993-12-27
Category : Mathematics
ISBN : 0582219779

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Generalized Fractional Calculus and Applications by Virginia S Kiryakova Pdf

In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.

Mittag-Leffler Functions, Related Topics and Applications

Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei Rogosin
Mittag Leffler Functions Related Topics and Applications Book PDF

Author : Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei Rogosin
Publisher : Springer Nature
Page : 548 pages
File Size : 42,8 Mb
Release : 2020-10-27
Category : Science
ISBN : 9783662615508

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Mittag-Leffler Functions, Related Topics and Applications by Rudolf Gorenflo,Anatoly A. Kilbas,Francesco Mainardi,Sergei Rogosin Pdf

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.

Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations

Sergey I Piskarev,Alexey V Ovchinnikov
Attractors Shadowing And Approximation Of Abstract Semilinear Differential Equations Book PDF

Author : Sergey I Piskarev,Alexey V Ovchinnikov
Publisher : World Scientific
Page : 213 pages
File Size : 50,6 Mb
Release : 2023-07-05
Category : Mathematics
ISBN : 9789811272790

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Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations by Sergey I Piskarev,Alexey V Ovchinnikov Pdf

The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.

Fractional-in-Time Semilinear Parabolic Equations and Applications

Ciprian G. Gal,Mahamadi Warma
Fractional in Time Semilinear Parabolic Equations and Applications Book PDF

Author : Ciprian G. Gal,Mahamadi Warma
Publisher : Springer Nature
Page : 193 pages
File Size : 46,7 Mb
Release : 2020-09-23
Category : Mathematics
ISBN : 9783030450434

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Fractional-in-Time Semilinear Parabolic Equations and Applications by Ciprian G. Gal,Mahamadi Warma Pdf

This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics. Besides classical examples involving the Laplace operator, subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov) boundary conditions, the framework also includes non-standard diffusion operators of "fractional" type, subject to appropriate boundary conditions. This book is aimed at graduate students and researchers in mathematics, physics, mathematical engineering and mathematical biology, whose research involves partial differential equations.

Fractional Dynamics

Vasily E. Tarasov
Fractional Dynamics Book PDF

Author : Vasily E. Tarasov
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 50,7 Mb
Release : 2011-01-04
Category : Science
ISBN : 9783642140037

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Fractional Dynamics by Vasily E. Tarasov Pdf

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

Applications Of Fractional Calculus In Physics

Rudolf Hilfer
Applications Of Fractional Calculus In Physics Book PDF

Author : Rudolf Hilfer
Publisher : World Scientific
Page : 473 pages
File Size : 49,8 Mb
Release : 2000-03-02
Category : Science
ISBN : 9789814496209

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Applications Of Fractional Calculus In Physics by Rudolf Hilfer Pdf

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.