Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development.
This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena.
The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians.
Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear.
Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces.
- Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems
- Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists
- The book provides the necessary background material required to go further into the subject and explore the rich research literature
Researchers and graduate students working in research, seminars, and advanced graduate courses in pure and applied mathematics, physics, mechanics, engineering, biology, and other applied sciences.
- Chapter 1: Preliminaries
- 1.1 Basic Facts and Notation
- 1.2 Fractional Integrals and Derivatives
- 1.3 Semigroups and Almost Sectorial Operators
- 1.4 Spaces of Asymptotically Periodic Functions
- 1.5 Weak Compactness of Sets and Operators
- 1.6 Multivalued Analysis
- 1.7 Stochastic Process
- Chapter 2: Fractional Evolution Equations
- 2.1 Cauchy Problems
- 2.2 Bounded Solutions on Real Axis
- 2.3 Notes and Remarks
- Chapter 3: Fractional Evolution Inclusions with Hille-Yosida Operators
- 3.1 Existence of Integral Solutions
- 3.2 Topological Structure of Solution Sets
- 3.3 Notes and Remarks
- Chapter 4: Fractional Control Systems
- 4.1 Existence and Optimal Control
- 4.2 Optimal Feedback Control
- 4.3 Controllability
- 4.4 Approximate Controllability
- 4.5 Topological Structure of Solution Sets
- 4.6 Notes and Remarks
- Chapter 5: Fractional Stochastic Evolution Inclusions
- 5.1 Existence of Mild Solutions
- 5.2 Topological Structure of Solution Sets
- 5.3 Notes and Remarks
- No. of pages:
- © Academic Press 2016
- 8th January 2016
- Academic Press
- eBook ISBN:
- Hardcover ISBN:
Professor Yong Zhou is a recognized expert in the field of non-linear difference equations and their applications in China. He was Editor-in-Chief of Journal of Dynamical Systems and Differential Equations over 2007-2011, and is present Guest Editor at Optimization (T&F), Nonlinear Dynamics and Journal of Vibration and Control (Sage), and at Elsevier former Guest Editor of Computers & Mathematics with Applications over 2010-2012 and Applied Mathematics and Computation over 2014-2015.
Faculty of Mathematics and Computer Sciences, Zhejiang Normal University, P.R. China.
"The style is lively and rigorous and the exposure is clear. The relevant historical comments and suggestive overviews may increase interest in this work. The reader will see how the existing techniques used in the study of "classical" differential equations can be adapted to the cases of fractional di erential equations studied in the book." --MathSciNet
"...a helpful book for those who have some familiarity with the continuous fractional calculus as well as differential inclusions, but wish to learn about some of the recent research in the area." --Zentralblatt MATH, Fractional Evolution Equations and Inclusions