Fractional Calculus UC Merced

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Fractional Calculus Day @ UC Merced YangQuan Chen, Ph.D., Director, MESA (Mechatronics, Embedded Systems and Automation)Lab MEAM/EECS, School of Engineering, University of California, Merced E: yqchen@ieee.org; or, yangquan.chen@ucmerced.edu T: (209)228-4672; O: SE1-254; Lab: Castle #22 (T: 228-4398) Castle Research Facility, UC Merced June 12, 2013

WELCOME! I’m very glad you are here! 6/12/2013 Fractional Calculus Day @ UC Merced. June 12, 2013

Welcome and Introduction History 2005, 2007, 2009, 2011 Utah State University 2013 UC Merced FC Day @ xxx is spreading as chain reactions … http://people.tuke.sk/igor.podlubny/FC-Day-at-TUKE/ http://people.tuke.sk/igor.podlubny/FC-Day-at-IST-20120703/ http://mechatronics.ece.usu.edu/foc/event/FOC_Day@USU/index.html 6/12/2013 Fractional Calculus Day @ UC Merced. June 12, 2013

“Fractional Calculus”: What and Why? Differentiation and integration of non-integer orders; Real power of Laplace operator “s” – such as 1/s0.5 , known as “half-order integrator” Tremendous potential in engineering applications and science discoveries. Connecting lots of dots when things are “complex” or “anomalous”. See a talk: https://vimeo.com/61141696 6/12/2013 Fractional Calculus Day @ UC Merced. June 12, 2013

Fractional Calculus Day @ UC Merced. June 12, 2013 Conclusion of Talk Fractional-Order Calculus Integer-Order Calculus Slide credit: Richard L. Magin, ICCC12 Fractional Calculus Day @ UC Merced. June 12, 2013 6/12/2013 5

Discrete gears vs. constantly-variable transmission Earth/moon Integer-Order Calculus Fractional-Order Calculus Discrete gears vs. constantly-variable transmission http://spectrum.ieee.org/energywise/energy/renewables/could-mechanics-best-power-electronics-in-evs Slide credit: Calvin Coopmans, 2/28/2013 email comment 6/12/2013 Fractional Calculus Day @ UC Merced. June 12, 2013

Fractional Calculus Day @ UC Merced. June 12, 2013 A snap shot of discussion board of Igor Podlubny and YangQuan Chen in Sept. 2005 Fractional Calculus Day @ UC Merced. June 12, 2013 6/12/2013

MESA Research Areas/Strengths Unmanned Aerial Systems and UAV-based Personal Remote Sensing (PRS) Cyber-Physical Systems (CPS) Modeling and Control of Renewable Energy Systems Mechatronics Applied Fractional Calculus (AFC) 6/12/2013 Fractional Calculus Day @ UC Merced. June 12, 2013

Fractional Calculus Day @ UC Merced. June 12, 2013 6/12/2013 Fractional Calculus Day @ UC Merced. June 12, 2013

Fractional Calculus Day @ UC Merced. June 12, 2013 6/12/2013 Fractional Calculus Day @ UC Merced. June 12, 2013