Fixed Point Methods in Fractional Differential Equations: A Practical Introduction with Examples

This book is devoted to the analytical study of the existence and uniqueness of solutions to fractional-order differential equations. It provides a rigorous theoretical framework that leverages various fixed point theorems to establish the well-posedness of these equations. The exposition begins by introducing the necessary mathematical foundations in functional analysis and fractional calculus, including definitions of the Riemann-Liouville and Caputo operators, as well as relevant special functions. Subsequently, the book systematically applies fixed point theorems to derive and prove existence and uniqueness results for different classes of fractional differential equations, providing a solid and comprehensive mathematical basis for their analysis. By focusing on the mathematical theory, this book serves as a robust foundation for understanding the powerful applications of fractional calculus across science and engineering.