This book outlines the theory, techniques and applications of fractional control. It covers fractional calculus with real, complex and variable orders, fractional transfer functions, fractional identification and pseudo-state-space representations. The control systems explored include: fractional lead control; fractional lag control; first, second and third generation Crone control; fractional PID, PI and PD control; fractional sliding mode control; logarithmic phase Crone control; fractional reset control; fractional H2 and H [plus/minus infinity] control; fractional predictive control; trajectory planning; fractional time-varying control. Each chapter contains solved examples, where the subject addressed is either expanded or applied to concrete cases. Common definitions and proofs are included, along with a bibliography, and a discussion of how MATLAB can be used to assist in the design and implementation of fractional control. --