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 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:  ≤2 and 0<  ≤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? 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 Tadeusz Kaczorek Białystok Technical University Faculty of Electrical Engineering Białystok, Poland

Future research problems

Future research problems (2) book: T. Kaczorek: Positive 1D and 2D systems. Springer Verlag ) Predictive control of fractional systems (chemical industry) 4) Adaptive control of fractional systems