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
1
 x  D
p ,  x, t     G ,       px, t 
t
t

G ,  u   F
1
E  t





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
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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?
2
t
d r
m 2    t   F r , v , d
dt
0
• 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