Impulsive Differential Equations And Inclusions

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Impulsive Differential Equations And Inclusions

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Author : Mouffak Benchohra
language : en
Publisher: Hindawi Publishing Corporation
Release Date : 2006

Impulsive Differential Equations And Inclusions written by Mouffak Benchohra and has been published by Hindawi Publishing Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations categories.

Impulsive Differential Inclusions

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Author : John R. Graef
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31

Impulsive Differential Inclusions written by John R. Graef and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-31 with Mathematics categories.

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Impulsive Differential Equations

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Author : N Perestyuk
language : en
Publisher: World Scientific
Release Date : 1995-08-31

Impulsive Differential Equations written by N Perestyuk and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-31 with Science categories.

Contents:General Description of Impulsive Differential SystemsLinear SystemsStability of SolutionsPeriodic and Almost Periodic Impulsive SystemsIntegral Sets of Impulsive SystemsOptimum Control in Impulsive SystemsAsymptotic Study of Oscillations in Impulsive SystemsA Periodic and Almost Periodic Impulsive SystemsBibliographySubject Index Readership: Researchers in nonlinear science. keywords:Differential Equations with Impulses;Linear Systems;Stability;Periodic and Quasi-Periodic Solutions;Integral Sets;Optimal Control “… lucid … the book … will benefit all who are interested in IDE…” Mathematics Abstracts

Impulsive Differential Equations And Inclusions

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Author :
language : en
Publisher:
Release Date : 2006

Impulsive Differential Equations And Inclusions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations categories.

This book is devoted to the rapidly developing theory of differential equations and inclusions with special emphasis on such equations and inclusions subject to impulses. In addition, the book includes a wide account of various applications to physical problems.

Fractional Order Equations And Inclusions

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Author : Michal Fečkan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-11-07

Fractional Order Equations And Inclusions written by Michal Fečkan 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 2017-11-07 with Mathematics categories.

This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions

Existence Theory For Nonlinear Ordinary Differential Equations

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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan 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 2013-04-17 with Mathematics categories.

We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.

Implicit Fractional Differential And Integral Equations

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Author : Saïd Abbas
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05

Implicit Fractional Differential And Integral Equations written by Saïd Abbas 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 2018-02-05 with Mathematics categories.

This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

Topics In Fractional Differential Equations

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Author : Saïd Abbas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-17

Topics In Fractional Differential Equations written by Saïd Abbas 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 2012-08-17 with Mathematics categories.

​​​ Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. ​​Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media such as porous media. It has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. Some equations present delays which may be finite, infinite, or state-dependent. Others are subject to an impulsive effect. The above problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. This book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. ​

Differential Equations With Impulse Effects

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Author : Nikolai A. Perestyuk
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-27

Differential Equations With Impulse Effects written by Nikolai A. Perestyuk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-27 with Mathematics categories.

Significant interest in the investigation of systems with discontinuous trajectories is explained by the development of equipment in which significant role is played by impulsive control systems and impulsive computing systems. Impulsive systems are also encountered in numerous problems of natural sciences described by mathematical models with conditions reflecting the impulsive action of external forces with pulses whose duration can be neglected. Differential equations with set-valued right-hand side arise in the investigation of evolution processes in the case of measurement errors, inaccuracy or incompleteness of information, action of bounded perturbations, violation of unique solvability conditions, etc. Differential inclusions also allow one to describe the dynamics of controlled processes and are widely used in the theory of optimal control. This monograph is devoted to the investigation of impulsive differential equations with set-valued and discontinuous right-hand sides. It is intended for researchers, lecturers, postgraduate students, and students of higher schools specialized in the field of the theory of differential equations, the theory of optimal control, and their applications.