Fractional Calculus with Applications in Mechanics —— Vibrations and Diffusion Processes

----- 分数阶微积分及在力学中的应用：从细胞到生态系统

ISBN: 9781848214170 出版年：2014 页码：331 Teodor M Atanackovic Stevan Pilipovic Wiley

This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and variational Hamilton–type principles. Mathematical rigor will be observed in the applications. The authors provide some problems formulated in the classical setting and some in the distributional setting. The solutions to these problems are presented in analytical form and these solutions are then analyzed numerically. Theorems on the existence of solutions will be presented for all examples discussed. In using various constitutive equations the restrictions following from the second law of thermodynamics will be implemented. Finally, the physical implications of obtained solutions will be discussed in detail.