Fractional calculus for scientists and engineers

✍ Scribed by Manuel Duarte Ortigueira (auth.)

• Publisher: Springer Netherlands
• Year: 2011
• Tongue: English
• Leaves: 114
• Series: Lecture Notes in Electrical Engineering 84
• Edition: 1
• Category: Library

✦ Synopsis

In recent years fractional calculus has been rediscovered by scientists and engineers and applied in an increasing number of fields, such as electromagnetism, control engineering, and signal processing. The increase in the number of physical and engineering processes that are best described by fractional differential equations has motivated its study.

This book gives a practical overview of Fractional Calculus as it relates to Signal Processing.� It is designed to be accessible by Scientists and Engineers mainly interested in applications, who do not want to spend too much time and effort to access to the main Fractional Calculus features and tools.� Readers can benefit from the attempt to present a Fractional Calculus foundation based of the Gr�nwald-Letnikov derivative, because it exhibits great coherence allowing deduction from it the other derivatives, which appear as a consequence of the Gr�nwald-Letnikov derivative properties and not as a prescription.

�

✦ Table of Contents

Front Matter....Pages i-xiv
A Travel Through the World of Fractional Calculus....Pages 1-3
The Causal Fractional Derivatives....Pages 5-41
Integral Representations....Pages 43-69
Fractional Linear Shift-Invariant Systems....Pages 71-99
Two-Sided Fractional Derivatives....Pages 101-121
The Fractional Quantum Derivative and the Fractional Linear Scale Invariant Systems....Pages 123-144
Where are We Going To?....Pages 145-152

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering; Signal, Image and Speech Processing; Mathematics of Computing