3rd IFAC Workshop on Fractional Differentiation and its Applications 20:45-21:30 Round Table Unsolved research problems in FC.
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3rd IFAC Workshop on Fractional Differentiation and its Applications 20:45-21:30 Round Table Unsolved research problems in FC
• Enrico Scalas • Complete characterization of the diffusive limit of continuous time random walks • What stochastic process do we have in the limit: Lévy Processes fully characterized =2, =1 (Bachelier-Wiener process) <2, =1 (Lévy flights) ≤2, <1
p
,
G
,
F t
1 1
E
G
t
,
x
t
p
But what about other finite dimensional distributions?
• Francesco Mainardi
• The fundamental solution of the fractional diffusion equation of order ≤2 in space and order 0< <2 in time admits a probability interpretation as a spatial probability density function (pdf) evolving in time if: 1 ≤2 and 0< ≤1 2 1 ≤ ≤2 For case 1) Gorenflo and Mainardi were able to provide random work models. For case 2) is a open problem.
• Possible use of FC to verify the foundation of the Riemann conjecture....
• Om Agrawal • Organization and its purpose and scope, Website • Applications – Should contain simple mathematics • Education – Courses at graduate and undergraduate level • Journal – Current problems and solutions • Specific Problems: • Analytical and numerical solution of fractional differential equations containing both forward and backward derivatives • Design of programmable fractional order controllers and their applications • Fractional optimal control • New fractional variational calculus and applications of new operators
• Tenreiro Machado • To find simple applications of FC • To have simple courses on FC • To include in the FC community new scientific areas and new members • Web repository of FC papers • To develop FC industrial products
• Raoul Nigmatullin • A possibility to derive Newton’s equation with memory?
m d
2
r dt
2
t
0
t
r
,
v
,
d
• Generalization of uncertainty principle containing an arbitrary moment • How to relate power – law exponent with thermodynamics (p,T,v) - ?
• CRONE team • To create a board that will manage and synchronize FC activities in the IFAC working group • To create an
e
-letter on the FC activities • To extend FC concepts in the area on nonlinear systems • To establish a test benchmark • To develop FC industrial applications
• Dumitru Baleanu • The physical meaning of Fractional derivatives • Consistent construction of fractional quantum mechanics, fractional quantum field theory, fractional differential geometry • Fractional variational principles with delay • Experimental evidences and manifestations of fractional dynamics in complex systems
• Blas Vinagre • To find ways of collaboration between groups working on the same topics
Future research problems
Future research problems
Tadeusz Kaczorek Białystok Technical University Faculty of Electrical Engineering Białystok, Poland e-mail: [email protected]
Future research problems
Future research problems (2)
book: T. Kaczorek: Positive 1D and 2D systems. Springer Verlag 2004 3) Predictive control of fractional systems (chemical industry) 4) Adaptive control of fractional systems