Fractional Differential Equations: Numerical Methods for Applications: 258 (Studies in Systems, Decision and Control, 258)

This book provides a comprehensive set of practical tools for exploring and discovering the world of fractional calculus and its applications, and thereby a means of bridging the theory of fractional differential equations (FDE) with real-world facts.These tools seamlessly blend centuries old numerical methods such as Gaussian quadrature that have stood the test of time with pioneering concepts such as hypermatrix equations to harness the emerging capabilities of modern scientific computing environments.This unique fusion of old and new leads to a unified approach that intuitively parallels the classic theory of differential equations, and results in methods that are unprecedented in computational speed and numerical accuracy. The opening chapter is an introduction to fractional calculus that is geared towards scientists and engineers.The following chapter introduces the reader to the key concepts of approximation theory with an emphasis on the tools of numerical linear algebra.The thi