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15 produkter
15 produkter
Häftad, Engelska, 2019
966 kr
Skickas inom 10-15 vardagar
The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades. This book provides an easy to read concise introduction to the theory of ill-posed abstract Volterra integro-differential equations. A major part of the research is devoted to the study of various types of abstract (multi-term) fractional differential equations with Caputo fractional derivatives, primarily from their invaluable importance in modeling of various phenomena appearing in physics, chemistry, engineering, biology and many other sciences. The book also contributes to the theories of abstract first and second order differential equations, as well as to the theories of higher order abstract differential equations and incomplete abstract Cauchy problems, which can be viewed as parts of the theory of abstract Volterra integro-differential equations only in its broad sense. The operators examined in our analyses need not be densely defined and may have empty resolvent set. Divided into three chapters, the book is a logical continuation of some previously published monographs in the field of ill-posed abstract Cauchy problems. It is not written as a traditional text, but rather as a guidebook suitable as an introduction for advanced graduate students in mathematics or engineering science, researchers in abstract partial differential equations and experts from other areas. Most of the subject matter is intended to be accessible to readers whose backgrounds include functions of one complex variable, integration theory and the basic theory of locally convex spaces. An important feature of this book as compared to other monographs and papers on abstract Volterra integro-differential equations is, undoubtedly, the consideration of solutions, and their hypercyclic properties, in locally convex spaces. Each chapter is further divided in sections and subsections and, with the exception of the introductory one, contains a plenty of exam
Inbunden, Engelska, 2026
2 941 kr
Kommande
Inbunden, Engelska, 2015
2 687 kr
Skickas inom 10-15 vardagar
The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades. This book provides an easy to read concise introduction to the theory of ill-posed abstract Volterra integro-differential equations. A major part of the research is devoted to the study of various types of abstract (multi-term) fractional differential equations with Caputo fractional derivatives, primarily from their invaluable importance in modeling of various phenomena appearing in physics, chemistry, engineering, biology and many other sciences. The book also contributes to the theories of abstract first and second order differential equations, as well as to the theories of higher order abstract differential equations and incomplete abstract Cauchy problems, which can be viewed as parts of the theory of abstract Volterra integro-differential equations only in its broad sense. The operators examined in our analyses need not be densely defined and may have empty resolvent set. Divided into three chapters, the book is a logical continuation of some previously published monographs in the field of ill-posed abstract Cauchy problems. It is not written as a traditional text, but rather as a guidebook suitable as an introduction for advanced graduate students in mathematics or engineering science, researchers in abstract partial differential equations and experts from other areas. Most of the subject matter is intended to be accessible to readers whose backgrounds include functions of one complex variable, integration theory and the basic theory of locally convex spaces. An important feature of this book as compared to other monographs and papers on abstract Volterra integro-differential equations is, undoubtedly, the consideration of solutions, and their hypercyclic properties, in locally convex spaces. Each chapter is further divided in sections and subsections and, with the exception of the introductory one, contains a plenty of exam
E-bok
PDF, Engelska, 20151 113 kr
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The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades. This book provides an easy to read concise introduction to the theory of ill-posed abstract Volterra integro-differential equations. A major part of the research is devoted to the study of various types of abstract (multi-term) fracti
E-bok
PDF, Engelska, 20203 512 kr
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The theory of linear topological dynamics is a rapidly growing field of research over the last three decades or so. This book presents a survey of recent results of the author obtained in this field during the period 2016-2019. Without any doubt, this is the first research monograph concerning the topological dynamics of multivalued operators and binary relations, especially, multivalued linear woperators, simple graphs, digraphs and tournaments (we feel duty bound to say that multivalued topological dynamics is still a very undeveloped field of investigation, full of open problems and possible for further expansion). Asiede from that, the main purpose of this monograph is to consider topologically dynamical properties of linear single-valued operators in Frechet spaces and abstract fractional differential equations in Frechet spaces, which could be degenerate or non-degenerate in time variable. In this monograph, we use only two types of fractional derivatives, namely the Caputo time-fractional derivatives and Weyl time-fractional derivatives. However, most results on dynamics of differential equations are given to the abstract differential equations with integer order derivatives, especially those of first and second order in time. The monograph is consistsed of two chapters; the first chapter is further broken down into nine sections, while the second chapter is broken down into seven sections. It is not of introductory character to linear topological dynamics and it is not written in a traditional manner. As in all my previously published monographs, the numbering of definitions, theorems, propositions, remarks, lemmas, corollaries, definitions, etc., are by chapter and section; the bibliography is by author in alphabetic order. Concerning target audience, wWe deeply believe that the book could be of invaluable help to experts in linear topological dynamics, researchers in abstract partial differential equations but and also to PhD students and advanced graduate students in mathematics as well. A potential reader should be familiar with backgrounds including elementary functional analysis, measure and integration theory as well as the basic theory of abstract (degenerate) Volterra integro-differential equations. At some places, the knowledge of graph theory is preferable but not demandedable. This monograph is not intended to be a comprehensive review of current trends; albeit includes several recent results from the field of linear topological dynamics and has more than 450 titles, our reference list is far from being exhaustively complete.
Inbunden, Engelska, 2019
1 893 kr
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This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.
E-bok
Engelska, 20191 928 kr
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This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.
E-bok
PDF, Engelska, 20191 911 kr
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This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.
Inbunden, Engelska, 2021
2 791 kr
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Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.
E-bok
PDF, Engelska, 20212 725 kr
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Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.
E-bok
Engelska, 20212 750 kr
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Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.
Inbunden, Engelska, 2023
1 961 kr
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The theory of almost periodic functions is a very active field of research for scholars. This research monograph analyzes various classes of multi-dimensional metrically almost periodic type functions with values in complex Banach spaces. We provide many applications of our theoretical results to the abstract Volterra integro-differential inclusions in Banach spaces.
E-bok
PDF, Engelska, 20231 917 kr
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The theory of almost periodic functions is a very active field of research for scholars. This research monograph analyzes various classes of multi-dimensional metrically almost periodic type functions with values in complex Banach spaces. We provide many applications of our theoretical results to the abstract Volterra integro-differential inclusions in Banach spaces.
1 987 kr
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The theory of almost periodic functions is a very active field of research for scholars. This research monograph analyzes various classes of multi-dimensional metrically almost periodic type functions with values in complex Banach spaces. We provide many applications of our theoretical results to the abstract Volterra integro-differential inclusions in Banach spaces.
Inbunden, Engelska, 2025
2 162 kr
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Maybe for the first time in the existing literature, we investigate here the almost periodic type solutions to the abstract Volterra difference equations depending on several variables. We also investigate the generalized almost periodic type sequences and their applications in a rather detailed manner as well as many new important spaces of (metrically) generalized almost periodic type spaces of sequences and functions. We essenitally apply some results from the theory of C-regularized solution operator families to the abstract Volterra integro-differential-difference equations, contributing also to the theory of fractional calculus and fractional differential equations. The theory of abstract Volterra integro-differential equations and the theory of abstract Volterra difference equations are very attractive fields of research of many authors. The almost periodic features and the asymptotically almost periodic features of solutions to the abstract Volterra differential-difference equations in Banach spaces have been sought in many research articles published by now. The main aim of this monograph is to continue the work collected in my monographs published with W. de Gruyter recently by providing several new results about the existence and uniqueness of almost periodic type solutions to the abstract Volterra integro-differential-difference equations which could be solvable or unsolvable with respect to the highest derivative (order). We would like to particularly emphasize that this is probably the first research monograph devoted to the study of almost periodic type solutions to the abstract Volterra difference equations depending on several variables. We also consider here many new important spaces of (metrically) generalized almost periodic type spaces of sequences and functions, and their almost automorphic analogues. It is also worth noting that this is probably the first research monograph which concerns the generalized almost periodic type sequences and their applications in a rather detailed manner; for the first time in the existing literature, we also present here some applications of results from the theory of $C$-regularized solution operator families to the abstract Volterra difference equations. Fractional calculus and discrete fractional calculus are rapidly growing fields of theoretical and applied mathematics, which are incredibly important in modeling of various real phenomena appearing in different fields like aerodynamics, rheology, interval-valued systems, chaotic systems with short memory and image encryption and discrete-time recurrent neural networks. Many important research results regarding the abstract fractional differential equations and the abstract fractional difference equations in Banach spaces have recently been obtained by a great number of authors from the whole world. In this monograph, we also contribute to the theories of (discrete) fractional calculus, fractional differential-difference equations and multi-dimensional Laplace transform. Although the monograph is far from being complete, we have decided to quote almost eight hundred and fifty research articles which could be of some importance to the interested readers for further developments of the theory established here.