Boundary Value Problems for Systems of Differential, Difference and Fractional Equations

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations
Author: Johnny Henderson
Publisher: Academic Press
Total Pages: 323
Release: 2015-10-30
Genre: Mathematics
ISBN: 0128036796

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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

Boundary Value Problems For Fractional Differential Equations And Systems

Boundary Value Problems For Fractional Differential Equations And Systems
Author: Bashir Ahmad
Publisher: World Scientific
Total Pages: 468
Release: 2021-02-18
Genre: Mathematics
ISBN: 9811224471

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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.

Boundary Value Problems for Fractional Differential Equations and Systems

Boundary Value Problems for Fractional Differential Equations and Systems
Author: Bashir Ahmad
Publisher: World Scientific Publishing Company
Total Pages: 468
Release: 2021
Genre: Boundary value problems
ISBN: 9789811224454

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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.

Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations

Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations
Author: A.K. Aziz
Publisher: Academic Press
Total Pages: 380
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483267997

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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.

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations
Author: Uri M. Ascher
Publisher: SIAM
Total Pages: 620
Release: 1994-12-01
Genre: Mathematics
ISBN: 9781611971231

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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.

Boundary Value Problems for Second-Order Finite Difference Equations and Systems

Boundary Value Problems for Second-Order Finite Difference Equations and Systems
Author: Johnny Henderson
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 120
Release: 2023-01-30
Genre: Mathematics
ISBN: 3111040453

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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.

Boundary Value Problems for Second-Order Finite Difference Equations and Systems

Boundary Value Problems for Second-Order Finite Difference Equations and Systems
Author: Johnny Henderson
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 168
Release: 2023-01-30
Genre: Mathematics
ISBN: 3111040372

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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.

New Trends in Differential and Difference Equations and Applications

New Trends in Differential and Difference Equations and Applications
Author: Feliz Manuel Minhós
Publisher: MDPI
Total Pages: 198
Release: 2019-10-14
Genre: Mathematics
ISBN: 3039215388

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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.

Focal Boundary Value Problems for Differential and Difference Equations

Focal Boundary Value Problems for Differential and Difference Equations
Author: R.P. Agarwal
Publisher: Springer Science & Business Media
Total Pages: 302
Release: 2013-03-09
Genre: Mathematics
ISBN: 9401715688

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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.

Fractional Differential Equations, Inclusions and Inequalities with Applications

Fractional Differential Equations, Inclusions and Inequalities with Applications
Author: Sotiris K. Ntouyas
Publisher: MDPI
Total Pages: 518
Release: 2020-11-09
Genre: Mathematics
ISBN: 3039432184

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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.