Almost Periodic And Almost Automorphic Solutions To Integro Differential Equations
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Almost Periodic And Almost Automorphic Solutions To Integro Differential Equations
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-05-06
Almost Periodic And Almost Automorphic Solutions To Integro Differential Equations written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-06 with Mathematics categories.
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.
Almost Periodicity And Almost Automorphy
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Author : Abdallah Afoukal
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03
Almost Periodicity And Almost Automorphy written by Abdallah Afoukal and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Mathematics categories.
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an “ordinary differential equation” with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.
Selected Topics In Almost Periodicity
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22
Selected Topics In Almost Periodicity written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.
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.
Metrical Almost Periodicity And Applications To Integro Differential Equations
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-06-06
Metrical Almost Periodicity And Applications To Integro Differential Equations written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Mathematics categories.
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.
Almost Periodic Type Solutions
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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03
Almost Periodic Type Solutions written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Mathematics categories.
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.
Almost Automorphic Type And Almost Periodic Type Functions In Abstract Spaces
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Author : Toka Diagana
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Almost Automorphic Type And Almost Periodic Type Functions In Abstract Spaces written by Toka Diagana and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses.
The Golden Anniversary Celebration Of The National Association Of Mathematicians
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Author : Omayra Ortega
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-12-10
The Golden Anniversary Celebration Of The National Association Of Mathematicians written by Omayra Ortega and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-10 with Education categories.
This volume is put together by the National Association of Mathematicians to commemorate its 50th anniversary. The articles in the book are based on lectures presented at several events at the Joint Mathematics Meeting held from January 16–19, 2019, in Baltimore, Maryland, including the Claytor-Woodard Lecture as well as the NAM David Harold Blackwell Lecture, which was held on August 2, 2019, in Cincinnati, Ohio.
Nonlinear Analysis Geometry And Applications
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Author : Diaraf Seck
language : en
Publisher: Springer Nature
Release Date : 2024-05-22
Nonlinear Analysis Geometry And Applications written by Diaraf Seck and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-22 with Mathematics categories.
The NLAGA's Biennial International Research Symposium (NLAGA-BIRS) is intended to gather African expertises in Nonlinear Analysis, Geometry and their Applications with their international partners in a four days conference where new mathematical results are presented and discussed. This book features the best papers presented during this Biennial. The different topics addressed are related to Partial Differential Equations, Differential inclusions, Geometrical Analysis of Optimal Shapes, Complex Analysis, Geometric Structures, Algebraic Geometry, Algebraic, Optimization, Optimal Control and Mathematical modeling. The main focus of the NLAGA project is to deepen and consolidate the development in West and Center Africa of Nonlinear Analysis, Geometry and their Applications, aimed at solving in particular real-world problems such as coastal erosion, urban network, pollution problems, and population dynamics.
Integro Differential Equations
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Author : Mouffak Benchohra
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-08-19
Integro Differential Equations written by Mouffak Benchohra and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-19 with Technology & Engineering categories.
This book delves into semilinear evolution equations, impulsive differential equations, and integro-differential equations with different types of delay. The main objective is to investigate the existence of solutions and explore their approximate controllability, complete controllability, and attractivity. The study involves boundary conditions, nonlocal conditions, and impulsive conditions. The analysis presented in this book goes beyond traditional solutions and encompasses the study of solutions that are asymptotically almost automorphic and integro-differential equations with impulsive effects in both bounded and unbounded domains. The book also contains applications to nuclear physics, elementary particle physics, chemical engineering, and economics. This book is intended for researchers and professionals in the field of mathematics, physics and industrial engineering, as well as advanced graduate students.
Advanced Topics On Semilinear Evolution Equations
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Author : Mouffak Benchohra
language : en
Publisher: World Scientific
Release Date : 2025-01-07
Advanced Topics On Semilinear Evolution Equations written by Mouffak Benchohra and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-07 with Mathematics categories.
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of 'Differential Evolution Equations' emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fréchet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.