Functional Fractional Calculus for System Identification and Controls [electronic resource] / by Shantanu Das.Material type: TextLanguage: English Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008Description: online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540727033Subject(s): Engineering | Global analysis (Mathematics) | Mathematics | Systems theory | Mathematical physics | Physics | Engineering mathematics | Engineering | Appl.Mathematics/Computational Methods of Engineering | Mathematical and Computational Physics | Analysis | Complexity | Applications of Mathematics | Systems Theory, ControlAdditional physical formats: Printed edition:: No titleDDC classification: 519 LOC classification: TA329-348TA640-643Online resources: Click here to access online
to Fractional Calculus -- Functions Used in Fractional Calculus -- Observation of Fractional Calculus in Physical System Description -- Concept of Fractional Divergence and Fractional Curl -- Fractional Differintegrations: Insight Concepts -- Initialized Differintegrals and Generalized Calculus -- Generalized Laplace Transform for Fractional Differintegrals -- Application of Generalized Fractional Calculus in Electrical Circuit Analysis -- Application of Generalized Fractional Calculus in Other Science and Engineering Fields -- System Order Identification and Control.
When a new extraordinary and outstanding theory is stated, it has to face criticism and skepticism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its applications to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. Historically, Sir Issac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J. Von. Neumann remarked, "…the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking." The XXI century will thus have ‘exact thinking’ for advancement in technology by growing application of fractional calculus, and this century will speak the language which nature understand the best.