Theory and applications of non-integer order systems : 8th Conference on Non-integer Order Calculus and Its Applications, Zakopane, Poland

• Corporate Author: Conference on Non-Integer Order Calculus and Its Applications Zakopane, Poland
• Other Authors: Babiarz, Artur (Editor), Czornik, Adam (Editor), Klamka, Jerzy (Editor), Niezabitowski, Michał (Editor)
• Format: Electronic eBook
• Language: English
• Published: Cham, Switzerland : Springer, [2017]
• Series: Lecture notes in electrical engineering ; v. 407.
• Subjects: Derivatives (Mathematics) > Congresses.; Fractional calculus > Congresses.; elektronické knihy; electronic books
• ISBN: 9783319454740; 9783319454733
• ISSN: 1876-1100 ;
• Physical Description: 1 online resource (xii, 512 pages) : illustrations

This book collects papers from the 8th Conference on Non-Integer Order Calculus and Its Applications that have been held on September 20-21, 2016 in Zakopane, Poland. The preceding two conferences were held in Szczecin, Poland in 2015, and in Opole, Poland, in 2014. This conference provides a platfo...

Table of Contents:

• Preface; Organization; Program Committee; Organizing Committee; Contents; Mathematical Foundations; Existence of Solutions of Abstract Fractional Impulsive Integrodifferential Equations of Sobolev Type; 1 Introduction; 2 Preliminaries; 3 Main Results; 4 Conclusion; References; Quadrature Based Approximations of Non-integer Order Integrator on Finite Integration Interval; 1 Introduction; 2 Diffusive Realization of Non-integer Order Integrator; 3 Approximation of Diffusive Realizations; 4 Quadratures on Infinite Intervals; 5 Approximation Analysis; 6 Conclusion; References.
• On the Fractional Continuous-Time Hegselmann
• Krause's Type Consensus Model1 Introduction and Preliminaries; 2 Consensus Formation; 3 Numerical Examples; References; Harmonic Numbers of Any Order and the Wolstenholme's-Type Relations for Harmonic Numbers; 1 New Definition of the Generalized Harmonic Numbers; 1.1 The Weyl Integral; 1.2 Poligamma Functions and Their Modifications; 1.3 Harmonic Numbers of Order r>1; 1.4 Selected Identities for the Generalized Harmonic Numbers; 2 Wolstenholme's-Type Relations for the Harmonic Numbers and the Generalized Harmonic Numbers.
• 2.1 Our Results
• Congruence Relations for the Harmonic Numbers and the Generalized Harmonic NumbersReferences; Cayley
• Hamilton Theorem for Fractional Linear Systems; 1 Introduction; 2 Preliminaries; 3 Cayley
• Hamilton Theorem for Fractional Continuous-Time linear Systems; 4 Cayley
• Hamilton Theorem for Discrete-Time Linear Systems; 5 Concluding Remarks; References; Order Composition Properties for Output-Additive Variable-Order Derivative; 1 Introduction; 2 Fractional-Order Grunwald
• Letnikov Type Derivative; 3 The Output-Additive Fractional Variable-Order Derivative.
• 4 The Output-Additive Switching Scheme5 Orders Composition Properties; 6 Numerical Results of Output-Additive Switching Scheme Composition with Fractional Constant-Order Differ-Integral; 7 Conclusions; References; Variable-, Fractional-Order Oscillation Element; 1 Introduction and Preliminaries; 1.1 Variable-, Fractional-Order Linear Integrator; 2 VFO Oscillation Element Description and Response; 3 VFOOE Stability and Oscillations Criteria; 4 Final Conclusions; References; Variable-, Fractional-Order Inertial Element; 1 Introduction; 2 Preliminaries; 3 VFO Inertial Element.
• 4 VFOIE Existence Conditions5 Numerical Examples; 6 Final Conclusions; References; Remarks on Mittag-Leffler Discrete Function and Putzer Algorithm for Fractional h-Difference Linear Equations; 1 Introduction; 2 Difference Fractional h-Operators; 3 Discrete Mittag-Leffler Function; 4 h-Difference Fractional Order Operators; 5 Putzer Algorithm; 6 Remarks on Mittag-Leffler Continuous Function for Caputo Operator; 7 Conclusions; References; On the Output-Additive Switching Strategy for a New Variable Type and Order Difference; 1 Introduction.