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3rd IFAC Workshop on Fractional Differentiation and its Applications 20:45-21:30 Round Table Unsolved research problems

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:

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3rd IFAC Workshop on Fractional Differentiation and its Applications 20:45-21:30 Round Table Unsolved research problems

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  1. 3rd IFAC Workshop on Fractional Differentiation and its Applications20:45-21:30 Round TableUnsolved research problems in FC

  2. 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?

  3. 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 • 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....

  4. 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

  5. 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

  6. RaoulNigmatullin • 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) - ?

  7. 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

  8. 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

  9. Blas Vinagre • To find ways of collaboration between groups working on the same topics

  10. Future research problems • Future research problems • Tadeusz Kaczorek • Białystok Technical University • Faculty of Electrical Engineering • Białystok, Poland • e-mail: kaczorek@isep.pw.edu.pl

  11. Future research problems

  12. 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

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