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

Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics


  • Author : Elina Shishkina
  • Publisher : Academic Press
  • Release Date : 2020-07-24
  • Genre: Mathematics
  • Pages : 592
  • ISBN 10 : 9780128204078

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

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 Book

Operator Theory and Harmonic Analysis


  • Author : Alexey N. Karapetyants
  • Publisher : Springer Nature
  • Release Date : 2021-09-27
  • Genre: Mathematics
  • Pages : 584
  • ISBN 10 : 9783030774936

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Operator Theory and Harmonic Analysis Excerpt :

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 Book

Direct and Inverse Sturm Liouville Problems


  • Author : Vladislav V. Kravchenko
  • Publisher : Springer Nature
  • Release Date : 2020-07-28
  • Genre: Mathematics
  • Pages : 154
  • ISBN 10 : 9783030478490

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Direct and Inverse Sturm Liouville Problems Excerpt :

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 Book

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


  • Author : Yeliz Karaca
  • Publisher : Academic Press
  • Release Date : 2022-07-01
  • Genre: Science
  • Pages : 350
  • ISBN 10 : 9780323886161

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Multi Chaos Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems Excerpt :

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 di

Mittag Leffler Functions  Related Topics and Applications Book

Mittag Leffler Functions Related Topics and Applications


  • Author : Rudolf Gorenflo
  • Publisher : Springer Nature
  • Release Date : 2020-10-27
  • Genre: Science
  • Pages : 540
  • ISBN 10 : 9783662615508

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Mittag Leffler Functions Related Topics and Applications Excerpt :

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 Book

Transmutation Operators and Applications


  • Author : Vladislav V. Kravchenko
  • Publisher : Springer Nature
  • Release Date : 2020-04-11
  • Genre: Mathematics
  • Pages : 686
  • ISBN 10 : 9783030359140

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Transmutation Operators and Applications Excerpt :

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 Book
Score: 3
From 2 Ratings

Theory and Applications of Fractional Differential Equations


  • Author : A.A. Kilbas
  • Publisher : Elsevier
  • Release Date : 2006-03-02
  • Genre: Mathematics
  • Pages : 523
  • ISBN 10 : 0444518320

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Theory and Applications of Fractional Differential Equations Excerpt :

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.

Fractional Calculus for Hydrology  Soil Science and Geomechanics Book

Fractional Calculus for Hydrology Soil Science and Geomechanics


  • Author : Ninghu Su
  • Publisher : CRC Press
  • Release Date : 2020-11-02
  • Genre: Science
  • Pages : 340
  • ISBN 10 : 9781351032407

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Fractional Calculus for Hydrology Soil Science and Geomechanics Excerpt :

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.

Basic Theory Book

Basic Theory


  • Author : Anatoly Kochubei
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2019-02-19
  • Genre: Mathematics
  • Pages : 489
  • ISBN 10 : 9783110571622

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Basic Theory Excerpt :

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.

Advanced Mathematical Methods Book

Advanced Mathematical Methods


  • Author : Francesco Mainardi
  • Publisher : MDPI
  • Release Date : 2020-02-05
  • Genre: Mathematics
  • Pages : 198
  • ISBN 10 : 9783039282463

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Advanced Mathematical Methods Excerpt :

The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the state-of-the-art of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.

Sturm Liouville Theory Book

Sturm Liouville Theory


  • Author : Werner O. Amrein
  • Publisher : Springer Science & Business Media
  • Release Date : 2005-12-05
  • Genre: Mathematics
  • Pages : 336
  • ISBN 10 : 9783764373597

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Sturm Liouville Theory Excerpt :

This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.

Mittag Leffler Functions  Related Topics and Applications Book

Mittag Leffler Functions Related Topics and Applications


  • Author : Rudolf Gorenflo
  • Publisher : Springer
  • Release Date : 2014-10-16
  • Genre: Mathematics
  • Pages : 443
  • ISBN 10 : 9783662439302

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Mittag Leffler Functions Related Topics and Applications Excerpt :

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.

Mathematical Reviews Book

Mathematical Reviews


  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 2004
  • Genre: Mathematics
  • Pages : null
  • ISBN 10 : UVA:X006180633

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Mathematical Reviews Excerpt :