Fuzzy Dynamic Equations on Time Scales. An Introduction with Applications

      Аннотация: Fuzzy Dynamic Equations on Time Scales is a text book written for Post graduate students and research scholars of Mathematics and Engineering. This book presents a brief introduction to the existence and uniqueness of solutions to fuzzy dynamic equations on time scales whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets in Euclidean space Rn under new class of derivatives called Hukuhara delta derivative and second type Hukuhara delta derivative which provides a foundation and framework for the nonlinear studies in the field of fuzzy dynamic equations on time scales. Beginning with the basics, the book first introduces fuzzy differential equations and dynamic equations on time scales. Fundamental topics such as fuzzy calculus and time scale calculus are discussed. Further introduced and studied the properties of Hukuhara delta derivative and second type Hukuhara delta derivative for fuzzy valued functions on time scales. Finally, sufficient conditions are established for the existence and uniqueness of solutions to fuzzy dynamic equations on time scales and results are illustrated with suitable examples.

Ключевые слова: Fuzzy Differential Equations, Dynamic Equations on time scales, Hukuhara derivative, delta derivative