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Variable order fractional derivatives Duarte Valrio 2017 / 9 / 7 - PowerPoint PPT Presentation

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Variable order fractional derivatives Duarte Valrio 2017 / 9 / 7 9/7/2017 Instituto Superior Tcnico Get the lecture notes from our site They are an introduction to some papers With the notes, you can find the papers of which I

  1. Variable order fractional derivatives Duarte Valério 2017 / 9 / 7 9/7/2017 Instituto Superior Técnico

  2. Get the lecture notes from our site • They are an introduction to some papers • With the notes, you can find the papers of which I am one of the authors • Look for the others in the net 9/7/2017 Instituto Superior Técnico

  3. Let’s define D a (t) f(t) in four cases: • a (t) is natural • a (t) is integer • a (t) is real • a (t) is complex 9/7/2017 Instituto Superior Técnico

  4. We will also talk about: • Matlab implementations • an application to bone remodelling dynamics • and other subjects too 9/7/2017 Instituto Superior Técnico

  5. Natural case 9/7/2017 Instituto Superior Técnico

  6. Switching after differentiating 9/7/2017 Instituto Superior Técnico

  7. 20 15 10 5 0 0 2 4 6 8 10 9/7/2017 Instituto Superior Técnico

  8. Switching before differentiating 9/7/2017 Instituto Superior Técnico

  9. 20 15 10 5 0 0 2 4 6 8 10 9/7/2017 Instituto Superior Técnico

  10. Switching both before and after 9/7/2017 Instituto Superior Técnico

  11. 20 15 10 5 0 0 2 4 6 8 10 9/7/2017 Instituto Superior Técnico

  12. Integer case 9/7/2017 Instituto Superior Técnico

  13. Switching after differentiating 9/7/2017 Instituto Superior Técnico

  14. 50 40 30 20 10 0 0 2 4 6 8 10 9/7/2017 Instituto Superior Técnico

  15. Switching before differentiating 9/7/2017 Instituto Superior Técnico

  16. 50 40 30 20 10 0 0 2 4 6 8 10 9/7/2017 Instituto Superior Técnico

  17. Switching both before and after 9/7/2017 Instituto Superior Técnico

  18. 50 40 30 20 10 0 0 2 4 6 8 10 9/7/2017 Instituto Superior Técnico

  19. Real case: constant orders 9/7/2017 Instituto Superior Técnico

  20. Real case: no memory 9/7/2017 Instituto Superior Técnico

  21. Real case: with memory 9/7/2017 Instituto Superior Técnico

  22. Real case: a different memory 9/7/2017 Instituto Superior Técnico

  23. Complex case: constant orders • GL definition works just the same 9/7/2017 Instituto Superior Técnico

  24. Complex case: no memory 9/7/2017 Instituto Superior Técnico

  25. Matlab toolboxes • Go to Matlab file exchange • Look for Duarte Valério • Look for Dominik Sierociuk 9/7/2017 Instituto Superior Técnico

  26. Bone remodelling • Osteoclasts destroy the bone • Osteoblasts rebuild the bone • The following scheme is from an upcoming paper: 9/7/2017 Instituto Superior Técnico

  27. Bone remodelling 9/7/2017 Instituto Superior Técnico

  28. Healthy bone vs. tumourous bone 9/7/2017 Instituto Superior Técnico

  29. Other topics • Variable order control • Distributed order control • Viscoelasticity • Anomalous diffusion 9/7/2017 Instituto Superior Técnico

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