Free PDF BookIntroduction to the Fractional Calculus of Variations

[Download.2KHO] Introduction to the Fractional Calculus of Variations

[Download.2KHO] Introduction to the Fractional Calculus of Variations

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Book Details :
Published on: 2012-11-14
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Original language: English

This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler-Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV. The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature. Readership: Advanced undergraduate, graduate students and researchers in mathematics, physics, operations research and applied sciences. Mathematical Problems by David Hilbert - Clark U Mathematical Problems Lecture delivered before the International Congress of Mathematicians at Paris in 1900 By Professor David Hilbert 1. Who of us would not be glad ... Fractional Calculus: Definitions and Applications - WKU FRACTIONAL CALCULUS: DEFINITIONS AND APPLICATIONS A Thesis Presented to The Faculty of the Department of Mathematics Western Kentucky University Fractional Calculus: History Denitions and Applications ... Fractional Calculus: History Denitions and Applications for the Engineer Adam Loverro Department of Aerospace and Mechanical Engineering University of Notre Dame Computing + Mathematical Sciences Course Descriptions Course Descriptions. Courses offered in our department for Applied and Computational Mathematics Control and Dynamical Systems and Computer Science are listed below. Index Numbers and Types of Index Numbers - eMathZone Introduction: Index numbers are meant to study the change in the effects of such factors which cannot be measured directly. According to Bowley Index numbers are ... Fractional calculus - Wikipedia Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers real number fractional powers or complex number ... Calculus of variations - Wikipedia Calculus of variations is a field of mathematical analysis that deals with maximizing or minimizing functionals which are mappings from a set of functions to the ... Fractional Calculus: differentiation and integration of ... Work of Euler: fractional calculus on monomials A year later (1730) Euler published some ideas for fractional calculus using the Gamma function in a natural way. Calculus -- from Wolfram MathWorld In general "a" calculus is an abstract theory developed in a purely formal way. "The" calculus more properly called analysis (or real analysis or in older ... Introduction to the Calculus of Variations Peter J. Olver ... IntroductiontotheCalculusofVariations by Peter J. Olver University of Minnesota 1. Introduction. Minimizationprinciples form one of the most wide-ranging means of ...
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