Fractional Differential Equations: Numerical Methods for Applications

ISBN-13: 9783030323769 / Angielski / Twarda / 2026 / 466 str.

Matthew Harker

Spis treści

Fractional Calculus and Fractional Differential Equations.- Essentials of Approximation Theory.- Numerical Approximation of Fractional Integrals and Derivatives.- Numerical Solution of Ordinary Fractional Differential Equations.- Numerical Solution of Partial Fractional Differential Equations.- Numerical Methods for Fractional Order Systems.- Reference Material.- Index.

Blurb

This book provides a comprehensive set of tools for exploring and discovering the world of fractional calculus and its applications, and in doing so offers a means of bridging the theory of fractional differential equations (FDE) and real-world facts. These tools unify quintessential numerical methods with pioneering concepts such as hypermatrix equations to harness the potential of the modern scientific computing environment.

Following an introduction to FDE aimed at scientists and engineers, the topics covered include the approximation of fractional order integrals and derivatives, the numerical solution of ordinary FDE, partial FDE in two, three, and four dimensions, and inverse problems for FDE, such as the all-important system identification problem.

As such, it equips students and researchers with reproducible methods that are unprecedented in speed and accuracy, which they can use to explore applications of FDE in areas such as viscoelasticity, bioengineering, and electrochemistry, to name but a few.