Abstract
A new type of derivative is introduced, whose order of differentiation is itself a dynamical variable. The order can be a continuous variable depending on the dependent x or independent t variables. We show that such variable order of differentiation can be approached with the theory of fractional integration and the associate variable order ordinary differential equations (VODE) can be solved as Volterra integral equations of second kind with singular integrable kernel. We find the conditions for existence and uniqueness of solutions of such VODE, and present some numeric solutions for particular cases exhibiting bifurcations and blow-up.
| Original language | American English |
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| State | Published - Sep 21 2016 |
| Event | Complex Systems Society - Amsterdam, The Netherlands Duration: Sep 21 2016 → … |
Conference
| Conference | Complex Systems Society |
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| Period | 9/21/16 → … |
Keywords
- dynamical systems
- complex systems
- variable scale
- variable memory
- selfa adapting dynamics
Disciplines
- Biomedical Engineering and Bioengineering
- Materials Science and Engineering
- Mechanical Engineering
- Life Sciences
- Physical Sciences and Mathematics
- Social and Behavioral Sciences