Thursday, June 10, 2010
Historical Introduction and the Concept of Fractional Derivatives
Presented by Siddarth Srinivasan | 
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A Not So Random Walk Through Historical Aspects of Fractional Calculus
Presented by Vivek Sharma | Download
Reading
- Sokolov, I. M., Klafter, J. and Blumen, A., Fractional Kinetics, Physics Today (2002). DOI:10.1063/1.1535007
- Friedrich, C., Schiessel, H. and Blumen, A., Constitutive Behavior Modeling and Fractional Derivatives, Rheology Series, 8, 429-466 (1999). DOI:10.1016/S0169-3107(99)80038-0
Friday, June 18, 2010
Simple Mechanical Fractional Derivative Models
Presented by Siddarth Srinivasan | Download
A Not So Random Walk Through Historical Aspects of Fractional Calculus (Part 2)
Presented by Vivek Sharma | Download
Tuesday, June 22, 2010
The Mittag Lefler Function and Stretched Exponentials
Presented by Thomas Ober | Download
Reading
- Metzler, R. and Klafter, J., From Stretched Exponential to Inverse Power Law: Fractional Dynamics, Cole-Cole Relaxation Processes and Beyond, Journal of Non-Crystalline Solids, 305, 81-87 (2002). DOI:10.1016/S0022-3093(02)01124-9
Friday, July 2, 2010
A Generalized Deborah Number
Presented by Ahmed Helal and Marc Fardin | Download
Reading
- Metzler, R. and Nonnenmacher, T. F., Fractional Relaxation Processes and Fractional Rheological Models for the Description of a Class of Viscoelastic Materials, International Journal of Plasticity, 19, 941-959 (2003). DOI:10.1016/S0749-6419(02)00087-6
Friday, July 9, 2010
Fractional Kinetics and Fractional Diffusion
Presented by Jason Rich | Download
Reading
- Metzler, R. and Klafter, J., The Random Walk's Guide to Anomalous Diffusion: A Fractional Dynamics Approach, Physics Reports, 339, 1-77 (2000). DOI:10.1016/S0370-1573(00)00070-3
Friday, July 16, 2010
Solving Fractional Differential Equations in MATLAB
Presented by Murat Ocalan | Download
Reading
- Podlubny, I. et al, Matrix Approach to Discrete Fractional Calculus II: Partial Fractional Differential Equations, Journal of Computational Physics, 228, 3137-3153 (2009). DOI:10.1016/j.jcp.2009.01.014
Wednesday, July 21, 2010
Fractal Gelation and Fractal Networks
Presentation by Chris Dimitriou | Download
Reading
- Warlus, S. and Ponton, A., A New Interpretation for the Dynamic Behaviour of Complex Fluids at the Sol–Gel Transition Using the Fractional Calculus, Rheologica Acta, 48, 51-58 (2009). DOI:10.1007/s00397-008-0306-z
Wednesday, July 28, 2010
Frame Invariant Version of Fractional Differential Models
Presented by Arezoo Ardekani | Download
Reading
- Drozdov, A. D., Fractional Differential Models in Finite Viscoelasticity, Acta Mechanica, 124, 155-180, (1997). DOI:10.1007/BF01213023
- Yang, P., Lam, Y. C. and Zhu, K.-Q., Constitutive Equation with Fractional Derivatives for the Generalized UCM Model, Journal of Non-Newtonian Fluid Mechanics, 165, 88-97 (2010). DOI:10.1016/j.jnnfm.2009.10.002
Friday, August 13, 2010
Fractional Calculus - The Murky Bits
A summary and clarification of certain aspects of the discussion over summer.
Presented by Aditya Jaishankar | Download
Reading
- Podlubny, I., Fractional Differential Equations, Mathematics in Science and Engineering V198, Academic Press (1999).
- Heymans, N. and Podlubny, I., Physical Interpretation of Initial Conditions for Fractional Differential Equations with Riemann-Liouville Fractional Derivatives, Rheologica Acta, 45, 765-771 (2006). DOI:10.1007/s00397-005-0043-5
- Yang, P., Lam, Y. C. and Zhu, K.-Q., Constitutive Equation with Fractional Derivatives for the Generalized UCM Model, Journal of Non-Newtonian Fluid Mechanics, 165, 88-97 (2010). DOI:10.1016/j.jnnfm.2009.10.002
- Friedrich, C. and Braun, H., Generalized Cole-Cole Behavior and Its Rheological Relevance, Rheologica Acta, 31, 309-322 (1992). DOI:10.1007/BF00418328
- Berberan-Santos, M. N., Properties of the Mittag-Leffler Relaxation Function, Journal of Mathematical Chemistry, 38, 629-635 (2005). DOI:10.1007/s10910-005-6909-z