Fixed-Point Methods for Fractional-Order Systems

This book presents recent advances in the estimation and control of nonlinear fractionalorder systems, viewed through the lens of fixedpoint theory. Fractionalorder models have gained importance for their ability to represent memory, hereditary properties, and complex system behavior with greater fidelity than classical integerorder approaches. Yet the nonlinear nature of these systems introduces analytical and numerical challenges.

The authors address these challenges by developing a unified framework grounded in fixedpoint theory, offering practical tools for stability analysis, numerical approximation, control design, and state estimation. Each chapter explains key concepts using a consistent structure and concludes with realworld examples, including applications in engineering, physics, and biological systems.

Designed for graduate students, researchers, and engineers working in control theory, applied mathematics, and nonlinear dynamics, this book provides a selfcontained and accessible introduction to contemporary methods for analyzing and controlling nonlinear fractionalorder systems.

Provides a selfcontained introduction that minimizes the need for additional background research Concludes most chapters with realworld applications, including examples from engineering and biological systems Presents all chapters in a consistent, readerfriendly style to support clear understanding

Autorentext

Rafael Martínez Guerra earned a B.Sc. in Physics and Mathematics from the National Polytechnic Institute (IPN), Mexico City, and an M.Sc. in Automatic Control from the Center for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav). He also obtained an M.Sc. in Mathematics and Automatic Control from École des Mines, Paris, and a Ph.D. from the Universidad Autónoma Metropolitana in 1996.

He is a Researcher in the Automatic Control Department at Cinvestav and has been a Level 3 Member of the National System of Researchers since 1992. He is the author or cöauthor of more than 92 journal articles, over 150 conference contributions, and 10 books. His research interests include nonlinear systems, differential geometric and differential algebraic methods, fractional order observers, fault detection and diagnosis, secure communications, synchronization, and chaos.

Lorenz OliväGonzalez obtained a B.Sc. in Control and Automation from the National Polytechnic Institute (IPN), Mexico City. He holds an M.Sc. (2022) and a Ph.D. (2026) in Automatic Control from the Center for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav). He is the author or cöauthor of 11 research articles published in international journals and conference proceedings. His research interests include fractional calculus, real and complex analysis, nonlinear dynamics, chaos theory, control theory, and numerical methods.

Inhalt

Introduction.- Essential overview.- A fixedpoint state estimator based on the conformable fractional order derivative.- Derivative free fixed point state estimators.- Fixed point numerical controller.- Fractional order proportional beta Integral state estimator.- Fractional order alpha differentiator.- A novel method for parameter identification.- An application to civil structures with beta.- A dynamic controller for quasi synchronization problem in fractional order chaotic systems.- Fault tolerant control and fault diagnosis.