Описание: Partial differential equations are one of the most used widely forms of mathematics in science and engineering. Two fractional PDEs can be considered, fractional in time, and fractional in space. These two volumes are directed to the development and use of SFPDEs, with the discussion divided into an introduction to Algorithms and Computer Coding in R and applications from classical integer PDEs.
Описание: Partial differential equations are one of the most used widely forms of mathematics in science and engineering. Two fractional PDEs can be considered, fractional in time, and fractional in space. This volume is directed to the development and use of SFPDEs, providing a discussion of applications from classical integer PDEs.
Автор: Michal Feckan, JinRong Wang, Michal Pospisil Название: Fractional-Order Equations and Inclusions ISBN: 3110521385 ISBN-13(EAN): 9783110521382 Издательство: Walter de Gruyter Цена: 22305.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics.
Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions
Автор: Varsha Daftardar-Gejji Название: Fractional Calculus and Fractional Differential Equations ISBN: 9811392269 ISBN-13(EAN): 9789811392269 Издательство: Springer Рейтинг: Цена: 27950.00 р. Наличие на складе: Поставка под заказ.
Описание: This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed.The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.
Автор: Alessandro Carbotti, Serena Dipierro, Enrico Valdinoci Название: Local Density of Solutions to Fractional Equations ISBN: 3110660695 ISBN-13(EAN): 9783110660692 Издательство: Walter de Gruyter Цена: 14495.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob . Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus , second edition (2020) Mariusz Lemanczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antic, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Автор: Anatoly Kochubei, Yuri Luchko Название: Fractional Differential Equations ISBN: 3110570823 ISBN-13(EAN): 9783110570823 Издательство: Walter de Gruyter Цена: 24165.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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 second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
Автор: Bashir Ahmad, Johnny L Henderson, Rodica Luca Название: Boundary Value Problems For Fractional Differential Equations And Systems ISBN: 9811224455 ISBN-13(EAN): 9789811224454 Издательство: World Scientific Publishing Рейтинг: Цена: 19008.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.
In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
Автор: Bashir Ahmad, Sotiris K Ntouyas Название: Nonlocal Nonlinear Fractional-order Boundary Value Problems ISBN: 9811230404 ISBN-13(EAN): 9789811230400 Издательство: World Scientific Publishing Рейтинг: Цена: 27720.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
There has been a great advancement in the study of fractional-order nonlocal nonlinear boundary value problems during the last few decades. The interest in the subject of fractional-order boundary value problems owes to the extensive application of fractional differential equations in many engineering and scientific disciplines. Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. This limitation led to the consideration of nonlocal and integral conditions which relate the boundary values of the unknown function to its values at some interior positions of the domain.
The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integro-differential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic.
This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope.
This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear SchrOdinger equations, fractional Landau-Lifshitz equations and fractional Ginzburg-Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs.
Автор: Dumitru Baleanu and Antonio Mendes Lopes Название: Handbook of Fractional Calculus with Applications ISBN: 3110570920 ISBN-13(EAN): 9783110570922 Издательство: Walter de Gruyter Рейтинг: Цена: 22439.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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 eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.
Автор: Manuel Duarte Ortigueira, Duarte Valerio Название: Fractional Signals and Systems ISBN: 3110621290 ISBN-13(EAN): 9783110621297 Издательство: Walter de Gruyter Цена: 22305.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The series is devoted to the publication of high-level monographs which cover progresses in fractional calculus research in mathematics and applications in physics, mechanics, engineering and biology etc. Methodological aspects e.g., theory, modeling and computational methods are presented from mathematical point of view, and emphases are placed in computer simulation, analysis, design and control of application-oriented issues in various scientific disciplines. It is designed for mathematicians, and researchers using fractional calculus as a tool in the field of physics, mechanics, engineering and biology. Contributions which are interdisciplinary and which stimulate further research at the crossroads of sciences and engineering are particularly welcomed.
Editor-in-chief: Changpin Li, Shanghai University, China
Editorial Board: Virginia Kiryakova, Bulgarian Academy of Sciences, Bulgaria Francesco Mainardi, University of Bologna, Italy Dragan Spasic, University of Novi Sad, Serbia Bruce Ian Henry, University of New South Wales, Australia YangQuan Chen, University of California, Merced, USA
Please submit book proposals to Professor Changpin Li: lcp@shu.edu.cn
Описание: Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus and provides a detailed treatment of existing numerical approximations.Theory and Numerical Approximations of Fractional Integrals and Derivatives presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results.The book’s core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.
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