Theory of Fuzzy Differential Equations and Inclusions

V. Lakshmikantham, Ram N. Mohapatra, Ram N. Mohapatra (University of Central Florida, Orlando, USA) , Ravi P. Agarwal (Florida Institute of Technology, Melbourne, USA)

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English

CRC Press
20 March 2003

Set theory; Discrete mathematics; Differential calculus & equations; Applied mathematics

Series: Mathematical Analysis and Applications

Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction

to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and provides a systematic account of recent developments. The chapters

are presented in a clear and logical way and include the preliminary material for fuzzy set theory; a description of calculus for fuzzy functions, an investigation of the basic theory of fuzzy differential equations, and an introduction to

fuzzy differential inclusions.

By: V. Lakshmikantham, Ram N. Mohapatra, Ram N. Mohapatra (University of Central Florida, Orlando, USA)
Series edited by: Ravi P. Agarwal (Florida Institute of Technology Melbourne USA)
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm, Spine: 16mm
Weight: 544g
ISBN: 9780415300735
ISBN 10: 0415300738
Series: Mathematical Analysis and Applications
Pages: 190
Publication Date: 20 March 2003
Audience: Professional and scholarly , Professional and scholarly , Professional & Vocational , Undergraduate , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Fuzzy Sets. The Hausdirfi Metric. Support Functions. The Space E^Tn. The Metric Space. Calculations of Fuzzy Functions. Convergence of Fuzzy Sets. Measurability. Integrability. Differentiability. Fundamental Theory. Initial Value Problem. Existence. Comparison Theorems. Convergence of Successive Approximations. Continuous Dependence. Global Existence. Approximate Solutions. Stability Criteria. Lyapunov-like Functions. Nonuniform Stability Criteria. Criteria for Boundedness. Fuzzy Differential Systems. The Method of Vector Lyapunov Functions. Linear Variation of Parameters Formula. Fuzzy Difference Equations. Impulsive Fuzzy Differential Equations. Fuzzy DEs with Delay. Hybrid Fuzzy Differential Equations. Fixed Points of Fuzzy Mappings. Boundary Value Problem. Fuzzy Equations of Volterra Type. A New Concept of Stability. Fuzzy Differential Inclusions. Formulation of FDIs. Differential Inclusions. Variation of Constants Formula. Fuzzy Volterra Integral Equations. Bibliography.

Lakshmikantham\, V.; Mohapatra\, Ram N.

Reviews for Theory of Fuzzy Differential Equations and Inclusions

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