​This book highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also summaries the latest findings, such as variable order derivative, distributed order derivative, and its applications. The book avoids lengthy mathematical demonstrations and presents the theories related to the applications in an easily readable manner. This textbook intends for students, researchers, and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.