Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales

ISBN-13: 9783031112355 / Angielski / Twarda / 2022 / 185 str.

Chao Wang;Ravi P. Agarwal

Opis

This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered.

Spis treści

Generalized Hukuhara Difference and Division for Interval and Fuzzy Arithmetic.- An Embedding Theorem and the Multiplication of Fuzzy Vectors.- Calculus of Fuzzy Vector-valued Functions on Time Scales.- Shift Almost Periodic Fuzzy Vector-valued Functions.- Division of Fuzzy Vector-valued Functions Depending on a Determinant Algorithm.- Almost Periodic Generalized Fuzzy Multidimensional Dynamic Equations and Applications.

O autorze

Chao Wang, Ph.D., is a Professor in the Department of Mathematics at Yunnan Univer-

sity. Dr. Wang has authored the books Theory of Translation Closedness for Time Scales and

Combined Measure and Shift Invariance Theory of Time Scales and Applications, both published

by Springer. His research focuses on the fields of nonlinear dynamic systems, control

theory, fuzzy dynamic equations, fractional differential equations, bifurcation theory,

nonlinear analysis, and numerical modeling.

Ravi P. Agarwal, Ph.D., is a Professor in the Department of Mathematics at the Texas A&M University-Kingsville. He completed his Ph.D. at the Indian Institute of Technology, Madras, India, in 1973.  Dr. Agarwal has authored or co-authored 50 books and 1,750 research articles.  His research interests include nonlinear analysis, differential and difference equations, fixed point theory, and general inequalities.

Blurb

This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems, including their continuous and discrete situations, but are also valid for other fuzzy multidimensional dynamic systems on various hybrid domains. In an effort to achieve more accurate analysis in real world applications, the authors propose a number of uncertain factors in the theory. As such, fuzzy dynamical models, interval-valued functions, differential equations, fuzzy-valued differential equations, and their applications to dynamic equations on time scales are considered. 

In addition, this book:

• Introduces readers to the almost periodic theory of fuzzy dynamical equations on time scales
• Presents comprehensive real-world applications in industrial engineering, systems science, and cybernetics
• Includes cutting-edge research results and a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems)