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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

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

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

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 platform for academic exchange on the theory and application of fractional calculus between domestic and international universities, research institutes, corporate experts and scholars. The Proceedings of the 8th Conference on Non-Integer Order Calculus and Its Applications 2016 brings together rigorously reviewed contributions from leading international experts. The included papers cover novel various important aspects of mathematical foundations of fractional calculus, modeling and control of fractional systems as well as controllability, detectability, observability and stability problems for this systems.