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Author : Arnaud Rougirel
Publisher : Springer Nature
ISBN 13 : 3031583566
Total Pages : 502 pages
Book Rating : 4.0/5 (315 download)
Download or read book Unified Theory for Fractional and Entire Differential Operators written by Arnaud Rougirel and published by Springer Nature. This book was released on with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yong Zhou
Publisher : World Scientific
ISBN 13 : 9811271704
Total Pages : 516 pages
Book Rating : 4.8/5 (112 download)
Download or read book Basic Theory Of Fractional Differential Equations (Third Edition) written by Yong Zhou and published by World Scientific. This book was released on 2023-10-06 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.
Author : C. Martinez
Publisher : Elsevier
ISBN 13 : 0080519075
Total Pages : 379 pages
Book Rating : 4.0/5 (85 download)
Download or read book The Theory of Fractional Powers of Operators written by C. Martinez and published by Elsevier. This book was released on 2001-01-17 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book makes available to researchers and advanced graduates a simple and direct presentation of the fundamental aspects of the theory of fractional powers of non-negative operators, which have important links with partial differential equations and harmonic analysis. For the first time ever, a book deals with this subject monographically, despite the large number of papers written on it during the second half of the century. The first chapters are concerned with the construction of a basic theory of fractional powers and study the classic questions in that respect. A new and distinct feature is that the approach adopted has allowed the extension of this theory to locally convex spaces, thereby including certain differential operators, which appear naturally in distribution spaces. The bulk of the second part of the book is dedicated to powers with pure imaginary exponents, which have been the focus of research in recent years, ever since the publication in 1987 of the now classic paper by G.Dore and A.Venni. Special care has been taken to give versions of the results with more accurate hypotheses, particularly with respect to the density of the domain or the range of the operator. The authors have made a point of making the text clear and self-contained. Accordingly, an extensive appendix contains the material on real and functional analysis used and, at the end of each chapter there are detailed historical and bibliographical notes in order to understand the development and current state of research into the questions dealt with.
Author : Kai Diethelm
Publisher : Springer
ISBN 13 : 3642145744
Total Pages : 251 pages
Book Rating : 4.6/5 (421 download)
Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer. This book was released on 2010-08-18 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Author : Giovanni C. Gentry
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781975838133
Total Pages : 370 pages
Book Rating : 4.8/5 (381 download)
Download or read book Basic Theory of Fractional Differential Equations written by Giovanni C. Gentry and published by Createspace Independent Publishing Platform. This book was released on 2014-05-14 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book is devoted to a rapidly developing area on the research of the qualitative theory of fractional differential equations. It is self-contained and unified in presentation, and provides readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the Picard operators technique, critical point theory and semigroups theory. Based on research work carried out by the author and other experts during the past four years, the contents are very new and comprehensive.
Author : Yong Zhou
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110769271
Total Pages : 342 pages
Book Rating : 4.1/5 (17 download)
Download or read book Theory of Fractional Evolution Equations written by Yong Zhou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-21 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.
Author : Stefan Bergman
Publisher : Springer Science & Business Media
ISBN 13 : 3642649858
Total Pages : 155 pages
Book Rating : 4.6/5 (426 download)
Download or read book Integral Operators in the Theory of Linear Partial Differential Equations written by Stefan Bergman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information.
Author : Francois Treves
Publisher :
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.3/5 (91 download)
Download or read book Distributions and General Theory of Differential Operators written by Francois Treves and published by . This book was released on 1960 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Juan J. Nieto
Publisher : MDPI
ISBN 13 : 3039217321
Total Pages : 172 pages
Book Rating : 4.0/5 (392 download)
Download or read book Fractional Differential Equations written by Juan J. Nieto and published by MDPI. This book was released on 2019-11-19 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.
Author : Igor Podlubny
Publisher : Elsevier
ISBN 13 : 0080531989
Total Pages : 366 pages
Book Rating : 4.0/5 (85 download)
Download or read book Fractional Differential Equations written by Igor Podlubny and published by Elsevier. This book was released on 1998-10-27 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3030869202
Total Pages : 422 pages
Book Rating : 4.0/5 (38 download)
Download or read book Unification of Fractional Calculi with Applications written by George A. Anastassiou and published by Springer Nature. This book was released on 2021-11-21 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications can be in applied sciences like geophysics, physics, chemistry, economics and engineering. This book is appropriate for researchers, graduate students, practitioners and seminars of the above disciplines, also to be in all science and engineering libraries.
Author : Adam Kubica
Publisher : Springer Nature
ISBN 13 : 9811590664
Total Pages : 134 pages
Book Rating : 4.8/5 (115 download)
Download or read book Time-Fractional Differential Equations written by Adam Kubica and published by Springer Nature. This book was released on 2020-11-29 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long, with its origins dating back to Leibniz. Since then, many great mathematicians, such as Abel, have made contributions that cover not only theoretical aspects but also physical applications of fractional calculus. The fractional partial differential equations govern phenomena depending both on spatial and time variables and require more subtle treatments. Moreover, fractional partial differential equations are highly demanded model equations for solving real-world problems such as the anomalous diffusion in heterogeneous media. The studies of fractional partial differential equations have continued to expand explosively. However we observe that available mathematical theory for fractional partial differential equations is not still complete. In particular, operator-theoretical approaches are indispensable for some generalized categories of solutions such as weak solutions, but feasible operator-theoretic foundations for wide applications are not available in monographs. To make this monograph more readable, we are restricting it to a few fundamental types of time-fractional partial differential equations, forgoing many other important and exciting topics such as stability for nonlinear problems. However, we believe that this book works well as an introduction to mathematical research in such vast fields.
Author : Sabir Umarov
Publisher : Springer
ISBN 13 : 3319207717
Total Pages : 446 pages
Book Rating : 4.3/5 (192 download)
Download or read book Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols written by Sabir Umarov and published by Springer. This book was released on 2015-08-18 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.
Author : Luisa Beghin
Publisher : Springer Nature
ISBN 13 : 3030692361
Total Pages : 308 pages
Book Rating : 4.0/5 (36 download)
Download or read book Nonlocal and Fractional Operators written by Luisa Beghin and published by Springer Nature. This book was released on 2021-07-23 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus. In particular, it collects scientific and original contributions to the development of the theory of nonlocal and fractional operators. Special attention is given to the applications in mathematical physics, as well as in probability. Numerical methods aimed to the solution of problems with fractional differential equations are also treated in the book. The contributions have been presented during the international workshop "Nonlocal and Fractional Operators", held in Sapienza University of Rome, in April 2019, and dedicated to the retirement of Prof. Renato Spigler (University Roma Tre). Therefore we also wish to dedicate this volume to this occasion, in order to celebrate his scientific contributions in the field of numerical analysis and fractional calculus. The book is suitable for mathematicians, physicists and applied scientists interested in the various aspects of fractional calculus.
Author : Vincenzo Ambrosio
Publisher : Springer Nature
ISBN 13 : 3030602206
Total Pages : 669 pages
Book Rating : 4.0/5 (36 download)
Download or read book Nonlinear Fractional Schrödinger Equations in R^N written by Vincenzo Ambrosio and published by Springer Nature. This book was released on 2021-04-19 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.
Author : D. E. Edmunds
Publisher : Springer
ISBN 13 : 3030021254
Total Pages : 324 pages
Book Rating : 4.0/5 (3 download)
Download or read book Elliptic Differential Operators and Spectral Analysis written by D. E. Edmunds and published by Springer. This book was released on 2018-11-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.
Author : Changpin Li
Publisher : SIAM
ISBN 13 : 1611975883
Total Pages : 326 pages
Book Rating : 4.6/5 (119 download)
Download or read book Theory and Numerical Approximations of Fractional Integrals and Derivatives written by Changpin Li and published by SIAM. This book was released on 2019-10-31 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, provides a detailed treatment of existing numerical approximations, and 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 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.
