Theory and Applications of Non-integer Order Systems : 8th Conference on Non-integer Order Calculus and Its Applications, Zakopane, Poland

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. Front Matter....Pages i-xii Front Matter....Pages 1-1 Existence of Solutions of Abstract Fractional Impulsive Integrodifferential Equations of Sobolev Type....Pages 3-10 Quadrature Based Approximations of Non-integer Order Integrator on Finite Integration Interval....Pages 11-20 On the Fractional Continuous-Time Hegselmann–Krause’s Type Consensus Model....Pages 21-32 Harmonic Numbers of Any Order and the Wolstenholme’s-Type Relations for Harmonic Numbers....Pages 33-44 Cayley–Hamilton Theorem for Fractional Linear Systems....Pages 45-55 Order Composition Properties for Output-Additive Variable-Order Derivative....Pages 57-64 Variable-, Fractional-Order Oscillation Element....Pages 65-75 Variable-, Fractional-Order Inertial Element....Pages 77-87 Remarks on Mittag-Leffler Discrete Function and Putzer Algorithm for Fractional h-Difference Linear Equations....Pages 89-99 On the Output-Additive Switching Strategy for a New Variable Type and Order Difference....Pages 101-111 Large Deviations for Stochastic Fractional Differential Equations....Pages 113-121 Mean Square Stability of Discrete-Time Fractional Order Systems With Multiplicative Noise....Pages 123-133 Front Matter....Pages 135-135 Conformable Fractional Wave-Like Equation on a Radial Symmetric Plate....Pages 137-146 Reconstruction Robin Boundary Condition in the Heat Conduction Inverse Problem of Fractional Order....Pages 147-156 Linear and Nonlinear Fractional Voigt Models....Pages 157-167 Digital Fractional Integrator....Pages 169-174 Optimal Control for Discrete Fractional Systems....Pages 175-185 Fractional Order Back Stepping Sliding Mode Control for Blood Glucose Regulation in Type I Diabetes Patients....Pages 187-202 Maximum and Minimum Principles for the Generalized Fractional Diffusion Problem with a Scale Function-Dependent Derivative....Pages 203-214 On a New Class of Multistage Fractional-Order Phase-Lead Compensators....Pages 215-225 Front Matter....Pages 135-135 On the Existence of Optimal Controls for the Fractional Continuous-Time Cucker–Smale Model....Pages 227-240 Determining the Time Elapsed Since Sudden Localized Impulse Given to Fractional Advection Diffusion Equation....Pages 241-251 Accuracy Analysis for Fractional Order Transfer Function Models with Delay....Pages 253-263 Accuracy Estimation of Digital Fractional Order PID Controller....Pages 265-275 Modeling of Fractional-Order Integrators and Differentiators Using Tustin-Based Approximations and Model Order Reduction Techniques....Pages 277-286 Tempered Fractional Model of Transient Current in Organic Semiconductor Layers....Pages 287-295 Modeling Heat Transfer Process in Grid-Holes Structure Changed in Time Using Fractional Variable Order Calculus....Pages 297-306 Analysis of Performance Indicators for Tuning Non-integer Order Controllers....Pages 307-317 Front Matter....Pages 319-319 Controllability of Nonlinear Fractional Delay Dynamical Systems with Multiple Delays in Control....Pages 321-332 New Controllability Criteria for Fractional Systems with Varying Delays....Pages 333-344 Controllability of Nonlinear Stochastic Fractional Integrodifferential Systems in Hilbert Spaces....Pages 345-355 Finding a Set of (A, B, C, D) Realisations for Fractional One-Dimensional Systems with Digraph-Based Algorithm....Pages 357-368 Relative Controllability of Nonlinear Fractional Delay Dynamical Systems with Time Varying Delay in Control....Pages 369-379 Stability Analysis for the New Model of Fractional Discrete-Time Linear State-Space Systems....Pages 381-389 Fractional Differential-Algebraic Systems with Delay: Computation of Final Dimension Initial Conditions and Inputs for Given Outputs....Pages 391-401 Front Matter....Pages 403-403 Robot Path Control with Al-Alaoui Rule for Fractional Calculus Discretization....Pages 405-418 Implementation of Bi-fractional Filtering on the Arduino Uno Hardware Platform....Pages 419-428 Fractional Prabhakar Derivative and Applications in Anomalous Dielectrics: A Numerical Approach....Pages 429-439 Finite Element Method for Time Fractional Keller–Segel Chemotaxis System....Pages 441-448 Adaptive Fractional Order Sliding Mode Controller Design for Blood Glucose Regulation-4-3....Pages 449-465 Front Matter....Pages 403-403 Expansion of Digraph Size of 1-D Fractional System with Delay....Pages 467-476 A Discrete-Time Fractional Order PI Controller for a Three Phase Synchronous Motor Using an Optimal Loop Shaping Approach....Pages 477-487 Application of SubIval, a Method for Fractional-Order Derivative Computations in IVPs....Pages 489-499 Application of the Time-Fractional Diffusion Equation to Methyl Alcohol Mass Transfer in Silica....Pages 501-510 Back Matter....Pages 511-512