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Theory of fuzzy differential equations and inclusions. (English) Zbl 1072.34001

Series in Mathematical Analysis and Applications 6. London: Taylor & Francis (ISBN 0-415-30073-8/hbk). ix, 178 p. (2003).
This monograph is devoted to the theory of fuzzy differential equations and inclusions. The book is organized in a highly self-contained and reader-friendly way and is devided into 6 chapters. In Chapter 1 (Fuzzy Sets), the authors include minimal background material sufficient to deal with the theory of fuzzy differential equations and inclusions. In Chapter 2 (Calculus of Fuzzy Functions), the necessary concepts and results related to the calculus of fuzzy functions are presented. In Chapter 3 (Fundamental Theory), the basic theory of fuzzy differential equations is investigated. A variety of comparison results for the solutions of fuzzy differential equations, which form the essential tools for studying the fundamental theory of fuzzy differential equations, are established. In Chapter 4 (Lyapunov-like Functions), the authors essentially investigate the stability theory via Lyapunov-like functions. The study of fuzzy differential systems is also initiated. In Chapter 5 (Miscellaneous Topics), the authors initiate several interesting topics, such as fuzzy difference equations, impulsive fuzzy differential equations, fuzzy differential equations with delay, hybrid fuzzy differential equations, fixed-points of fuzzy mappings, boundary value problems and fuzzy equations of Volterra type. Finally, in Chapter 6 (Fuzzy Differential Inclusions), fuzzy differential inclusions are discussed. A new formulation is introduced and results on stability and periodicity are provided. The bibliography contains 123 entries.

MSC:

34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
34G25 Evolution inclusions
34A60 Ordinary differential inclusions
34C25 Periodic solutions to ordinary differential equations
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