Boundary Value Problems For Systems Of Differential Difference And Fractional Equations

Author : Johnny Henderson,Rodica Luca
Publisher : Academic Press
Page : 322 pages
File Size : 42,6 Mb
Release : 2015-10-30
Category : Mathematics
ISBN : 9780128036792

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Boundary Value Problems for Systems of Differential, Difference and Fractional Equations by Johnny Henderson,Rodica Luca Pdf

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions Discusses second order difference equations with multi-point boundary conditions Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions

Author : Bashir Ahmad,Johnny L Henderson,Rodica Luca
Publisher : World Scientific
Page : 468 pages
File Size : 52,9 Mb
Release : 2021-02-18
Category : Mathematics
ISBN : 9789811224478

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Boundary Value Problems For Fractional Differential Equations And Systems by Bashir Ahmad,Johnny L Henderson,Rodica Luca Pdf

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.

Author : Johnny Henderson,Rodica Luca
Publisher : Walter de Gruyter GmbH & Co KG
Page : 120 pages
File Size : 46,7 Mb
Release : 2023-01-30
Category : Mathematics
ISBN : 9783111040455

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Boundary Value Problems for Second-Order Finite Difference Equations and Systems by Johnny Henderson,Rodica Luca Pdf

This is an indispensable reference for those mathematicians that conduct research activity in applications of fixed-point theory to boundary value problems for nonlinear difference equations. Coverage includes second-order finite difference equations and systems of second-order finite difference equations subject to diverse multi-point boundary conditions, and various methods to study the existence of positive solutions for these problems.

Author : A.K. Aziz
Publisher : Academic Press
Page : 380 pages
File Size : 54,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483267999

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Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by A.K. Aziz Pdf

Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.

Author : Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell
Publisher : SIAM
Page : 620 pages
File Size : 44,7 Mb
Release : 1994-12-01
Category : Mathematics
ISBN : 1611971233

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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell Pdf

This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.

Author : R.P. Agarwal
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 40,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401715683

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Focal Boundary Value Problems for Differential and Difference Equations by R.P. Agarwal Pdf

The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations. In this vast field of research, the conjugate (Hermite) and the right focal point (Abei) types of problems have received the maximum attention. This is largely due to the fact that these types of problems are basic, in the sense that the methods employed in their study are easily extendable to other types of prob lems. Moreover, the conjugate and the right focal point types of boundary value problems occur frequently in real world problems. In the monograph Boundary Value Problems for Higher Order Differential Equations published in 1986, we addressed the theory of conjugate boundary value problems. At that time the results on right focal point problems were scarce; however, in the last ten years extensive research has been done. In Chapter 1 of the mono graph we offer up-to-date information of this newly developed theory of right focal point boundary value problems. Until twenty years ago Difference Equations were considered as the dis cretizations of the differential equations. Further, it was tacitly taken for granted that the theories of difference and differential equations are parallel. However, striking diversities and wide applications reported in the last two decades have made difference equations one of the major areas of research.

Author : Herbert B. Keller
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 53,9 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9780486828343

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Numerical Methods for Two-Point Boundary-Value Problems by Herbert B. Keller Pdf

Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.

Author : Sotiris K. Ntouyas
Publisher : MDPI
Page : 518 pages
File Size : 52,6 Mb
Release : 2020-11-09
Category : Mathematics
ISBN : 9783039432189

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Fractional Differential Equations, Inclusions and Inequalities with Applications by Sotiris K. Ntouyas Pdf

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Author : Bashir Ahmad,Sotiris K Ntouyas
Publisher : World Scientific
Page : 597 pages
File Size : 45,7 Mb
Release : 2021-04-06
Category : Mathematics
ISBN : 9789811230424

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Nonlocal Nonlinear Fractional-order Boundary Value Problems by Bashir Ahmad,Sotiris K Ntouyas Pdf

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.

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 198 pages
File Size : 45,7 Mb
Release : 2019-10-14
Category : Mathematics
ISBN : 9783039215386

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New Trends in Differential and Difference Equations and Applications by Feliz Manuel Minhós,João Fialho Pdf

This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Author : Johnny Henderson,Rodica Luca
Publisher : Walter de Gruyter GmbH & Co KG
Page : 168 pages
File Size : 45,7 Mb
Release : 2023-01-30
Category : Mathematics
ISBN : 9783111040370

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Boundary Value Problems for Second-Order Finite Difference Equations and Systems by Johnny Henderson,Rodica Luca Pdf

This is an indispensable reference for those mathematicians that conduct research activity in applications of fixed-point theory to boundary value problems for nonlinear functional equations. Coverage includes second-order finite difference equations and systems of difference equations subject to multi-point boundary conditions, various methods to study the existence of positive solutions for difference equations, and Green functions.

Author : Leslie Fox
Publisher : Unknown
Page : 400 pages
File Size : 44,9 Mb
Release : 1957
Category : Boundary value problems
ISBN : UCAL:B4980144

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The Numerical Solution of Two-point Boundary Problems in Ordinary Differential Equations by Leslie Fox Pdf

Author : Iván Area,Alberto Cabada,José Ángel Cid,Daniel Franco,Eduardo Liz,Rodrigo López Pouso,Rosana Rodríguez-López
Publisher : Springer Nature
Page : 295 pages
File Size : 41,7 Mb
Release : 2019-09-19
Category : Mathematics
ISBN : 9783030269876

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Nonlinear Analysis and Boundary Value Problems by Iván Area,Alberto Cabada,José Ángel Cid,Daniel Franco,Eduardo Liz,Rodrigo López Pouso,Rosana Rodríguez-López Pdf

This book is devoted to Prof. Juan J. Nieto, on the occasion of his 60th birthday. Juan José Nieto Roig (born 1958, A Coruña) is a Spanish mathematician, who has been a Professor of Mathematical Analysis at the University of Santiago de Compostela since 1991. His most influential contributions to date are in the area of differential equations. Nieto received his degree in Mathematics from the University of Santiago de Compostela in 1980. He was then awarded a Fulbright scholarship and moved to the University of Texas at Arlington where he worked with Professor V. Lakshmikantham. He received his Ph.D. in Mathematics from the University of Santiago de Compostela in 1983. Nieto's work may be considered to fall within the ambit of differential equations, and his research interests include fractional calculus, fuzzy equations and epidemiological models. He is one of the world’s most cited mathematicians according to Web of Knowledge, and appears in the Thompson Reuters Highly Cited Researchers list. Nieto has also occupied different positions at the University of Santiago de Compostela, such as Dean of Mathematics and Director of the Mathematical Institute. He has also served as an editor for various mathematical journals, and was the editor-in-chief of the journal Nonlinear Analysis: Real World Applications from 2009 to 2012. In 2016, Nieto was admitted as a Fellow of the Royal Galician Academy of Sciences. This book consists of contributions presented at the International Conference on Nonlinear Analysis and Boundary Value Problems, held in Santiago de Compostela, Spain, 4th-7th September 2018. Covering a variety of topics linked to Nieto’s scientific work, ranging from differential, difference and fractional equations to epidemiological models and dynamical systems and their applications, it is primarily intended for researchers involved in nonlinear analysis and boundary value problems in a broad sense.

Author : John R Graef,Johnny Henderson,Lingju Kong Liu
Publisher : World Scientific
Page : 176 pages
File Size : 45,6 Mb
Release : 2018-02-13
Category : Electronic
ISBN : 9789813236479

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Ordinary Differential Equations and Boundary Value Problems by John R Graef,Johnny Henderson,Lingju Kong Liu Pdf

The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book. The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well. Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems. Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs. Contents: Systems of Differential EquationsContinuation of Solutions and Maximal Intervals of ExistenceSmooth Dependence on Initial Conditions and Smooth Dependence on a ParameterSome Comparison Theorems and Differential InequalitiesLinear Systems of Differential EquationsPeriodic Linear Systems and Floquet TheoryStability TheoryPerturbed Systems and More on Existence of Periodic Solutions Readership: Graduate students and researchers interested in ordinary differential equations. Keywords: Differential Equations;Linear Systems;Comparison Theorems;Differential Inequalities;Periodic Systems;Floquet Theory;Stability Theory;Perturbed Equations;Periodic SolutionsReview: Key Features: Clarity of presentationTreatment of linear and nonlinear problemsIntroduction to stability theoryNonroutine exercises to expand insight into more difficult conceptsExamples provided with thorough explanations

Author : Sandra Pinelas,John R. Graef,Stefan Hilger,Peter Kloeden,Christos Schinas
Publisher : Springer Nature
Page : 754 pages
File Size : 47,5 Mb
Release : 2020-10-21
Category : Mathematics
ISBN : 9783030563233

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Differential and Difference Equations with Applications by Sandra Pinelas,John R. Graef,Stefan Hilger,Peter Kloeden,Christos Schinas Pdf

This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.