Advances in Fractional Calculus

Part 1. Analytical and Numerical Techniques

1. Three Classes of FDEs Amenable to Approximation Using a Galerkin Technique
Satwinder Jit Singh, Anindya Chatterjee

2. Enumeration of the Real Zeros of the Mittag-Leffler Function Ea(z), 1 <a< 2
John W. Hanneken, David M. Vaught, B. N. Narahari Achar

3. The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equation
B. N. Narahari Achar, Carl F. Lorenzo, Tom T. Hartley

4. Comparison of Five Numerical Schemes for Fractional Differential Equations
Om Prakash Agrawal, Pankaj Kumar

5. Suboptimum H2 Pseudo-rational Approximations to Fractional-order Linear Time Invariant Systems
Dingyü Xue, YangQuan Chen

6. Linear Differential Equations of Fractional Order
Blanca Bonilla, Margarita Rivero, Juan J. Trujillo

7. Riesz Potentials as Centred Derivatives
Manuel Duarte Ortigueira

Part 2. Classical Mechanics and Particle Physics

8. On Fractional Variational Principles
Dumitru Baleanu, Sami I. Muslih

9. Fractional Kinetics in Pseudochaotic Systems and Its Applications
George M. Zaslavsky

10. Semi-integrals and Semi-derivatives in Particle Physics
Peter W. Krempl

11. Mesoscopic Fractional Kinetic Equations versus a Riemann–Liouville Integral Type
Raoul R. Nigmatullin, Juan J. Trujillo

Part 3. Diffusive Systems

12. Enhanced Tracer Diffusion in Porous Media with an Impermeable Boundary
N. Krepysheva, L. Di Pietro, M. C. Néel

13. Solute Spreading in Heterogeneous Aggregated Porous Media
Kira Logvinova, Marie Christine Néel

14. Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media
F. San Jose Martinez, Y. A. Pachepsky, W. J. Rawls

15. Modelling and Identification of Diffusive Systems using Fractional Models
Amel Benchellal, Thierry Poinot, Jean-Claude Trigeassou

Part 4. Modeling

16. Identification of Fractional Models from Frequency Data
Duarte Valério, José Sá da Costa

17. Dynamic Response of the Fractional Relaxor–Oscillator to a Harmonic Driving Force
B. N. Narahari Achar, John W. Hanneken

18. A Direct Approximation of Fractional Cole–Cole Systems by Ordinary First-order Processes
Markus Haschka, Volker Krebs

19. Fractional Multimodels of the Gastrocnemius Muscle for Tetanus Pattern
Laurent Sommacal, Pierre Melchior, Jean-Marie Cabelguen, Alain Oustaloup, Auke Ijspeert

20. Limited-Bandwidth Fractional Differentiator: Synthesis and Application in Vibration Isolation
Pascal Serrier, Xavier Moreau, Alain Oustaloup

Part 5. Electrical Systems

21. A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits
Cecília Reis, J. A. Tenreiro Machado, J. Boaventura Cunha

22. Electrical Skin Phenomena: A Fractional Calculus Analysis
J. A. Tenreiro Machado, Isabel S. Jesus, Alexandra Galhano, J. Boaventura Cunha, J. K. Tar

23. Implementation of Fractional-order Operators on Field Programmable Gate Arrays
Cindy X. Jiang, Joan E. Carletta, Tom T. Hartley

24. Complex Order-Distributions Using Conjugated order Differintegrals
Jay L. Adams, Tom T. Hartley, Carl F. Lorenzo

Part 6. Viscoelastic and Disordered Media

25. Fractional Derivative Consideration on Nonlinear Viscoelastic Statical and Dynamical Behavior under Large Pre-Displacement
Hiroshi Nasuno, Nobuyuki Shimizu, Masataka Fukunaga

26. Quasi-Fractals: New Possibilities in Description of Disordered Media
R. R. Nigmatullin, A. P. Alekhin

27. Fractional Damping: Stochastic Origin and Finite Approximations
Satwinder Jit Singh, Anindya Chatterjee

28. Analytical Modelling and Experimental Identification of Viscoelastic Mechanical Systems
Giuseppe Catania, Silvio Sorrentino

Part 7. Control

29. LMI Characterization of Fractional Systems Stability
Mathieu Moze, Jocelyn Sabatier, Alain Oustaloup

30. Active Wave Control for Flexible Structures Using Fractional Calculus
Masaharu Kuroda

31. Fractional-order Control of a Flexible Manipulator
Vicente Feliu, Blas M. Vinagre, Concepción A. Monje

32. Tuning Rules for Fractional PIDs
Duarte Valério, José Sá da Costa

33. Frequency Band-Limited Fractional Differentiator Prefilter in Path Tracking Design
Pierre Melchior, Alexandre Poty, Alain Oustaloup

34. Flatness Control of a Fractional Thermal System
Pierre Melchior, Mikaël Cugnet, Jocelyn Sabatier, Alexandre Poty, Alain Oustaloup

35. Robustness Comparison of Smith Predictor-based Control and Fractional-Order Control
Patrick Lanusse, Alain Oustaloup

36. Robust Design of an Anti-windup Compensated 3rd-Generation Crone Controller
Patrick Lanusse, Alain Oustaloup, Jocelyn Sabatier

37. Robustness of Fractional-order Boundary Control of Time Fractional Wave Equations with Delayed Boundary Measurement Using the Simple Predictor
Jinsong Liang, Weiwei Zhang, YangQuan Chen, Igor Podlubny

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