Fractal elements and their applications. (2017)

• Record Type: Book
• Further Information: Note: Anis Kharisovich Gil'mutdinov, Pyotr Arkhipovich Ushakov, Reyad El-Khazali ; ed. by A. Kh. Gil'mutdinov.
• Authors: Gil'mutdinov, Anis Kharisovich; Ushakov, Pyotr Arkhipovich; El-Khazali, Reyad
• Editors: Gil'mutdinov, Anis Kharisovich
• Contents: Foreword; Contents; Abbreviations; Chapter 1: Modeling of Fractal Elements and Processes; 1.1 Concept of Fractals, Self-Similarity, and Scaling; 1.2 Dimension Types; 1.3 Regular Fractals; 1.4 Irregular Random Fractals; 1.5 Multifractals; 1.6 Fractal Signals; 1.7 Physical Meaning of Hurst Parameter; 1.8 Relation Between Fractality and Spectrum Response; 1.9 Examples of Signal Analysis; Chapter 2: Fractal Calculus Fundamentals; 2.1 Preliminaries; 2.2 Properties of Fractional-Order Integrals and Derivatives; 2.2.1 Riemann-Liouville Fractional-Order Integral and Derivative. 2.2.2 Grunwald-Letnikov Fractional-Order Derivative and Integral2.2.3 Properties of Fractional-Order Derivatives; 2.3 Laplace Transform of Fractional-Order Operators; 2.3.1 Fundamentals of Laplace Transform; 2.3.2 Laplace Transform of Fractional-Order Integrals; 2.3.3 Laplace Transform of Fractional-Order Derivatives; 2.4 Fourier Transform of Fractional-Order Operators; 2.4.1 Fundamentals of Fourier Transform; 2.4.2 Fourier Transform of Fractional-Order Integrals; 2.4.3 Fourier Transform of Fractional-Order Derivatives; 2.5 Dynamics of Fractional-Order Transfer Functions. 2.5.1 Fractional-Order Transfer Functions2.5.2 Mittag-Leffler Function; 2.5.3 Solving Fractional-Order Differential Equation (FoDEQ) Using Laplace Transform; 2.6 Fractional-Order Electrical and Electronic Systems; 2.6.1 Semi-infinite Transmission Line; 2.6.2 Electrochemistry; 2.6.3 Rough Surface Impedance; Chapter 3: Fractal Elements; 3.1 Fractal Impedances and Fractal Element; 3.2 Implementation of Fractal Impedances Using Electrochemical Converters; 3.2.1 Liquid Electrolyte Electrochemical Signal Converters; 3.2.2 Solid Electrolyte Electrochemical Signal Converters. 3.2.3 Fractal Element Fractor3.3 Implementation of Fractal Impedances (Immittances) Using RC Circuits with Lumped Parameters; 3.3.1 Preliminaries; 3.3.2 Properties of Input RC-Transfer Functions; 3.3.3 Circuit Realization Using Foster Forms; 3.3.4 Circuit Realization Using Cauer Forms; 3.3.5 Rational Approximation of Fractal-Order Impedances; 3.3.5.1 The Oustaloup Method of Rational Approximation; 3.3.5.2 Shareff Method of Rational Approximation; 3.3.5.3 El-Khazali Approximation of Fractional-Order Integro-Differential Operators; 3.3.6 Realization of Fractional-Order Inductors (FoIs). 3.3.7 Realization of Fractional-Order Capacitors (FoC)3.4 Realization of Fractal Impedances Using RC Circuits with Distributed Parameters; 3.5 Fabrication of Fractal Impedances Using Nanostructured Materials; 3.6 Comparison of Fractal Element Characteristics Using Different Fabrication Technology; Chapter 4: Design and Implementation of Thin RC-EDP Films; 4.1 Classification of Static Heterogeneous Characteristics of RC-EDP Films; 4.2 RC-EDP Film Design of Multilayer Structure; 4.3 Design Development of RC-EDP Films by Changing Layers Geometry.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 515/.83; Engineering; Fractional calculus; Fractals; Systems engineering; Electronics; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Fractals; Fractional calculus; Technology & Engineering -- Electronics -- Circuits -- General; Technology & Engineering -- Electronics -- General; Circuits & components; Imaging systems & technology; Electronics engineering; Electronic books
• Languages: English
• ISBNs: 9783319452494; 3319452495
• Related ISBNs: 9783319452487; 3319452487
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed February 16, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.