Fixed-Point Methods for Fractional-Order Systems

This book presents recent advances in the estimation and control of nonlinear fractional-order systems, viewed through the lens of fixed-point theory. Fractional-order models have gained importance for their ability to represent memory, hereditary properties, and complex system behavior with greater fidelity than classical integer-order 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 fixed-point 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 real-world 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 self-contained and accessible introduction to contemporary methods for analyzing and controlling nonlinear fractional-order systems.