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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.

Calculus. --- Fractional calculus. --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Engineering mathematics. --- Global analysis (Mathematics). --- Mathematics. --- System theory. --- Mathematical and Computational Engineering. --- Theoretical, Mathematical and Computational Physics. --- Analysis. --- Complex Systems. --- Applications of Mathematics. --- Systems Theory, Control. --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Engineering --- Engineering analysis --- Systems, Theory of --- Systems science --- Mathematics --- Philosophy --- Systems theory. --- Applied mathematics. --- Mathematical physics. --- Mathematical analysis. --- Analysis (Mathematics). --- Statistical physics. --- Dynamical systems. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- 517.1 Mathematical analysis --- Physical mathematics --- Statistical methods