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The Averaging of Fuzzy Integrodifferential Equations on a Finite Interval
Abstract
In this article, we prove the substantiation of the method of averaging for the integro-differential equations with small parameter on the metric space (E n , D). Thereby we expand a circle of systems to which it is possible to apply Krylov-Bogolyubov method of averaging.
We develop the ideas of the method of averaging for some classes of fuzzy systems (fuzzy differential equations with delay, fuzzy differerntial equations with pulsed action, fuzzy integral equations, fuzzy differential inclusions, and differential inclusions with fuzzy right-hand sides without and with pulsed action).
In this paper, we will prove a possibility of use of the scheme of a full average at research of the linear fuzzy differential equations with a small parameter, when the right-hand side is 2π-periodic.
In this article we prove the substantiation of the method of full averaging for the fuzzy differential equations with small parameter on the metric space (En;D). Thereby we expand a circle of systems to which it is possible to apply Krylov-Bogolyubov method of averaging.
In the past several decades many significant results in averaging for systems of ODE's have been obtained. These results have not attracted a tention in proportion to their importance, partly because they have been overshadowed by KAM theory, and partly because they remain widely scattered - and often untranslated - throughout the Russian literature. The present book seeks to remedy that situation by providing a summary, including proofs, of averaging and related techniques for single and multiphase systems of ODE's. The first part of the book surveys most of what is known in the general case and examines the role of ergodicity in averaging. Stronger stability results are then obtained for the special case of Hamiltonian systems, and the relation of these results to KAM Theory is discussed. Finally, in view of their close relation to averaging methods, both classical and quantum adiabatic theorems are considered at some length. With the inclusion of nine concise appendices, the book is very nearly self-contained, and should serve the needs of both physicists desiring an accessible summary of known results, and of mathematicians seeing an introduction to current areas of research in averaging.
We study the existence and uniqueness of solutions and controllability for the semilinear fuzzy integrodifferential equations in n-dimensional fuzzy vector space (EN)n by using Banach fixed point theorem, that is, an extension of the result of J. H. Park et al. to n-dimensional fuzzy vector space.
In this paper, we study the ε-approximate controllability for the semilinear fuzzy integrodifferential control system in fuzzy vector space. This is an extension of result of Kwun et al.[4] to n-dimensional fuzzy vector space.
In this paper, the LU-representation of fuzzy number is considered and based on the LUrepresentation of fuzzy volterra integro-differential equation (FVIDE) is discussed. The existence of solution of FVIDE is brought in details. Then, the solution is found in three cases of FVIDE that is concluded from the kernel. Finally, the method is illustrated by solving two examples.
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