Introduction to Fractional Differential Equations

ISBN-13: 9783030008949 / Angielski / Twarda / 2018 / 188 str.

Constantin Milici; Gheorghe Draganescu; Jose Antonio Tenreiro Machado

Opis

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.

Recenzje

"The book is written nicely and useful as an introductory book on fractional differential equations. Important references are also provided at the end of each chapters. The main focus of the book is numerical methods. The book provides maple and mathematica codes, which can be very helpful to the readers interested in numerical simulations of such systems." (Syed Abbas, zbMath 1417.34004, 2019)

Spis treści

Introduction.- Special Functions.- Fractional derivative and integral.- The Laplace transform.- Fractional differential equations.- Generalized systems.- Numerical methods.

O autorze

Dr. Constantin Milici is a retired lecturer with the Department of Mathematics, Polytechnic University of Timișoara, Timisoara, Romania. Dr. Gheorghe Draganescu is a Prof Dr. with the Research Center in Theoretical Physics, West University of Timișoara, Timișoara, Romania. Dr. José António Tenreiro Machado is Principal Coordinator Professor with the Institute of Engineering of Porto, Porto, Portugal.

Blurb

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