Fractional Calculus for Scientists and Engineers: Lecture Notes in Electrical Engineering, cartea 84

1. Fractional Derivative.- 2. Integral representations.- 3. Fractional Linear Systems.- 4. Two sided fractional derivatives.- 5. The quantum fractional derivative and the scale invariant linear systems.- 6. Where do we go?

From the reviews:
“Fractional calculus--the theory of differential and integral operators of noninteger order--is an area of mathematics that has been neglected for a very long period of time. … Ortigueira provides a look at this theory from the point of view of someone working in signal processing. … it may be a book suitable for experts in signal processing who want to learn how they can use fractional calculus for the modeling of their circuits and systems … .” (Kai Diethelm, ACM Computing Reviews, October, 2011)

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.
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Provides a practical overview of Fractional Calculus Designed to be accessible by Scientists and Engineers mainly interested in applications Multidisciplinary presentation will be useful to researchers in fields such as electromagnetism, control engineering, and signal processing