Theory and Applications of Non-integer Order Systems

Part I. Mathematical Foundations

1. Existence of Solutions of Abstract Fractional Impulsive Integrodifferential Equations of Sobolev Type
Natarajan Annapoorani

2. Quadrature Based Approximations of Non-integer Order Integrator on Finite Integration Interval
Jerzy Baranowski

3. On the Fractional Continuous-Time Hegselmann–Krause’s Type Consensus Model
Ewa Girejko, Dorota Mozyrska, Małgorzata Wyrwas

4. Harmonic Numbers of Any Order and the Wolstenholme’s-Type Relations for Harmonic Numbers
Edyta Hetmaniok, Piotr Lorenc, Mariusz Pleszczyński, Michał Różański, Marcin Szweda, Roman Wituła

5. Cayley–Hamilton Theorem for Fractional Linear Systems
Tadeusz Kaczorek

6. Order Composition Properties for Output-Additive Variable-Order Derivative
Michał Macias

7. Variable-, Fractional-Order Oscillation Element
Dorota Mozyrska, Piotr Ostalczyk

8. Variable-, Fractional-Order Inertial Element
Piotr Ostalczyk, Dorota Mozyrska

9. Remarks on Mittag-Leffler Discrete Function and Putzer Algorithm for Fractional h-Difference Linear Equations
Ewa Pawłuszewicz

10. On the Output-Additive Switching Strategy for a New Variable Type and Order Difference
Dominik Sierociuk, Wiktor Malesza, Michał Macias

11. Large Deviations for Stochastic Fractional Differential Equations
Murugan Suvinthra

12. Mean Square Stability of Discrete-Time Fractional Order Systems With Multiplicative Noise
Viorica Mariela Ungureanu, Mădălina Roxana Buneci

Part II. Modeling and Control

13. Conformable Fractional Wave-Like Equation on a Radial Symmetric Plate
Derya Avcı, Beyza Billur İskender Eroğlu, Necati Özdemir

14. Reconstruction Robin Boundary Condition in the Heat Conduction Inverse Problem of Fractional Order
Rafał Brociek, Damian Słota, Adam Zielonka

15. Linear and Nonlinear Fractional Voigt Models
Amar Chidouh, Assia Guezane-Lakoud, Rachid Bebbouchi, Amor Bouaricha, Delfim F. M. Torres

16. Digital Fractional Integrator
Radosław Cioć

17. Optimal Control for Discrete Fractional Systems
Andrzej Dzieliński

18. Fractional Order Back Stepping Sliding Mode Control for Blood Glucose Regulation in Type I Diabetes Patients
Hamid Heydarinejad, Hadi Delavari

19. Maximum and Minimum Principles for the Generalized Fractional Diffusion Problem with a Scale Function-Dependent Derivative
Małgorzata Klimek, Kalina Kamińska

20. On a New Class of Multistage Fractional-Order Phase-Lead Compensators
Guido Maione

21. On the Existence of Optimal Controls for the Fractional Continuous-Time Cucker–Smale Model
Agnieszka B. Malinowska, Tatiana Odzijewicz, Ewa Schmeidel

22. Determining the Time Elapsed Since Sudden Localized Impulse Given to Fractional Advection Diffusion Equation
Marie-Christine Néel

23. Accuracy Analysis for Fractional Order Transfer Function Models with Delay
Krzysztof Oprzędkiewicz, Wojciech Mitkowski

24. Accuracy Estimation of Digital Fractional Order PID Controller
Krzysztof Oprzędkiewicz

25. Modeling of Fractional-Order Integrators and Differentiators Using Tustin-Based Approximations and Model Order Reduction Techniques
Marek Rydel, Rafał Stanisławski, Marcin Gałek, Krzysztof J. Latawiec

26. Tempered Fractional Model of Transient Current in Organic Semiconductor Layers
Renat Sibatov, Ekaterina Morozova

27. Modeling Heat Transfer Process in Grid-Holes Structure Changed in Time Using Fractional Variable Order Calculus
Piotr Sakrajda, Dominik Sierociuk

28. Analysis of Performance Indicators for Tuning Non-integer Order Controllers
Marta Zagórowska

Part III. Controllability and Stability

29. Controllability of Nonlinear Fractional Delay Dynamical Systems with Multiple Delays in Control
Krishnan Balachandran

30. New Controllability Criteria for Fractional Systems with Varying Delays
Jerzy Klamka, Beata Sikora

31. Controllability of Nonlinear Stochastic Fractional Integrodifferential Systems in Hilbert Spaces
Rajendran Mabel Lizzy

32. Finding a Set of (A, B, C, D) Realisations for Fractional One-Dimensional Systems with Digraph-Based Algorithm
Konrad Andrzej Markowski, Krzysztof Hryniów

33. Relative Controllability of Nonlinear Fractional Delay Dynamical Systems with Time Varying Delay in Control
Joice Nirmala Rajagopal

34. Stability Analysis for the New Model of Fractional Discrete-Time Linear State-Space Systems
Andrzej Ruszewski

35. Fractional Differential-Algebraic Systems with Delay: Computation of Final Dimension Initial Conditions and Inputs for Given Outputs
Zbigniew Zaczkiewicz

Part IV. Applications

36. Robot Path Control with Al-Alaoui Rule for Fractional Calculus Discretization
Artur Babiarz, Adrian Łȩgowski, Michał Niezabitowski

37. Implementation of Bi-fractional Filtering on the Arduino Uno Hardware Platform
Waldemar Bauer, Aleksandra Kawala-Janik

38. Fractional Prabhakar Derivative and Applications in Anomalous Dielectrics: A Numerical Approach
Roberto Garrappa, Guido Maione

39. Finite Element Method for Time Fractional Keller–Segel Chemotaxis System
Arumugam Gurusamy

40. Adaptive Fractional Order Sliding Mode Controller Design for Blood Glucose Regulation-4-3
Hamid Heydarinejad, Hadi Delavari

41. Expansion of Digraph Size of 1-D Fractional System with Delay
Konrad Andrzej Markowski, Krzysztof Hryniów

42. A Discrete-Time Fractional Order PI Controller for a Three Phase Synchronous Motor Using an Optimal Loop Shaping Approach
Paolo Mercorelli

43. Application of SubIval, a Method for Fractional-Order Derivative Computations in IVPs
Marcin Sowa

44. Application of the Time-Fractional Diffusion Equation to Methyl Alcohol Mass Transfer in Silica
Alexey A. Zhokh, Andrey A. Trypolskyi, Peter E. Strizhak

Keywords: Engineering, Control, Complexity