Introduction to Fractional Differential Equations - Milici, Constantin; Drăgănescu, Gheorghe; Tenreiro Machado, J.; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2019)
This book introduces a series of problems and methods insufficiently discussed in the field of Fractional Calculus - a major, emerging tool relevant to all areas of scientific inquiry. The authors present examples based on symbolic computation, written in Maple and Mathematica, and address both mathematical and computational areas in the context of mathematical modeling and the generalization of classical integer-order methods. Distinct from most books, the present volume fills the gap between mathematics and computer fields, and the transition from integer- to fractional-order methods. Introduces Fractional Calculus in an accessible manner, based on standard integer calculus Supports the use of higher-level mathematical packages, such as Mathematica or Maple Facilitates understanding the generalization (towards Fractional Calculus) of important models and systems, such as Lorenz, Chua, and many others Provides a simultaneous introduction to analytical and numerical methods in Fractional Calculus.
Introduction -- Special Functions -- Fractional derivative and integral -- The Laplace transform -- Fractional differential equations -- Generalized systems -- Numerical methods.
Keywords: Engineering mathematics; Mathematical optimization; Calculus of variations; Mathematical analysis; Dynamics; Nonlinear theories; Engineering Mathematics; Calculus of Variations and Optimization; Integral Transforms and Operational Calculus; Applied Dynamical Systems