This book presents the main tools for investigations of the existence and uniqueness of as well as the existence of multiple solutions for initial- and boundary-value problems for fuzzy impulsive dynamic equations on time scales.
Time-scale theory is relatively new. The basic theory attempts to unify both approaches of dynamic modeling: difference and differential equations. Similar ideas have been used before and go back in the introduction of the Riemann-Stieltjes integral, which unifies sums and integrals. Many results in differential equations easily carry over to the corresponding results for difference equations, while other results seem to be totally different in nature.
For these reasons, the theory of dynamic equations is an active area of research. The time scale calculus can be applied to any fields in which dynamic processes are described by discrete or continuous time models. The calculus of time scales has various applications involving noncontinuous domains such as certain insect populations, phytoremediation of metals, wound healing, maximization problems in economics, and traffic problems.
This book is intended for researchers and students in engineering and science. There are eight chapters in this book. The chapters in the book are organized in a way that is pedagogically accessible. Each chapter concludes with a section on practical problems to develop further understanding.
This book presents the main tools for investigations of the existence and uniqueness of as well as the existence of multiple solutions for initial- and boundary-value problems for fuzzy impulsive dynamic equations on time scales.
Chapter 1 Introduction.
Chapter 2 Fuzzy Calculus on Time Scales.
Chapter 3 Existence and Stability of First Order Fuzzy Impulsive Dynamic
Equations.
Chapter 4 Boundary Value Problems for First Order Fuzzy
Impulsive Dynamic Equations.
Chapter 5 Existence of Solutions of Second
Order Fuzzy Impulsive Dynamic Equations.
Chapter 6 Boundary Value Problems
for Second Order Fuzzy Impulsive Dynamic Equations.
Chapter 7 Oscillations
of Fuzzy Impulsive Dynamic Equations.
Chapter 8 Linear Fuzzy Impulsive
Dynamic Systems. Bibliography. Index
Svetlin Georgiev is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales.
Khaled Zennir earned his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. In 2015, he received his highest diploma in Habilitation in mathematics from Constantine University, Algeria. He is currently an assistant professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and longtime behavior.
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