1. MESA LAB On IFAC2014 Selected Two Papers Jianxiong Cao MESA LAB MESA (Mechatronics, Embedded Systems and Automation) LAB School of Engineering, University of California, Merced E: jcao6@ucmerced.edu Phone: 209-201-3819 Lab: CAS Eng 820 (T: 228-4398) September 8, 2014. Monday 16PM-18:00 PM Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

2. MESA LAB Outline AFC Workshop Series @ MESALAB @ UCMerced 09/11/2014 1. Papers that I am most interested 2. The main contributions of their work 3. Conclusion

3. MESA LAB Papers that I am interested AFC Workshop Series @ MESALAB @ UCMerced 08/28/2014 1.Discretization of Fractional-Order Differentiators and Integrators 2. Relation between fractional order models and diffusion in the body.

4. MESA LAB Main contributions Introduces a closed form discretization method of fractional- order differentiators or integrators. They generalize the Tustin operator to derive a stable and minimum 1 st and Second order discrete-time operators (DTO) that discretize continuous fractional differintegral operators. 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-4/1024 Paper I

5. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-5/1024 First order operator Second order operator

6. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-6/1024 Comparison with Dr. Chen’s work as a bench mark

7. MESA LAB Conclusion Both forms exhibit similar magnitude and phase responses. Using (13), the magnitude frequency deviation at low frequency is better than that of Dr. Chen’s method. While the phase response of Dr. Chen’s method at low frequency is better than that of (13). The significant improvement of (13) is that they used order reduction. 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-7/1024

8. MESA LAB Main contributions The paper presented the mathematical fundamental of fractional calculus in modeling of diffusion in the human body. The results reveal that fractional calculus are natural solutions for modeling complex phenomena in biological tissue. 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-8/1024 Paper II

9. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-9/1024

10. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-10/1024

11. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-11/1024

12. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-12/1024

13. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-13/1024

14. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-14/1024

15. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-15/1024

16. MESA LAB 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-16/1024

17. MESA LAB Conclusion 04/21/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-17/1024

18. MESA LAB 08/11/2014 AFC Workshop Series @ MESALAB @ UCMerced Slide-18/1024 Thank you for your attentions