Fractional Thermal Systems

We investigate the fractional behavior of the integrators associated with a fractional diffusion equation in an interface, in two different geometries, a wall and a sphere, by means of a new relation between Caputo derivatives and non integer integrators. The behavior of such integrators is shown using Bode diagrams calculated for a limited spectral range. At high frequencies, the fractional behavior is approximated by a non integer order integrator. As a particular case we recover some recent results. © 2011 IEEE.24732476University of Louisville,Ningbo University,Zhejiang Sci-Tech University,Communication University of China,Georgia State UniversityCaputo, M., The splitting of the free oscillations of the Earth caused by rheology (1990) Rend. Fis. Acc. Lincei, 1, pp. 119-125Luchko, Y.F., Rivero, M., Trujillo, J.J., Velasco, M.P., Fractional models, non-locality, and complex systems (2010) Comp. and Math. Appl., 59, pp. 1048-1056Magin, R., Ortigueira, M.D., Podlubny, I., Trujillo, J.J., On the fractional signals and systems (2011) Signal Processing, 91, pp. 350-371Mainardi, F., Mura, A., Pagnini, G., The M-Wright function in timefractional diffusion process: Tutorial survey (2010) Int. J. Diff. Eq., 2010. , ID 104505Barbosa, R.S., (1999) Algoritmos de Controlo de Ordem Não-inteira, , Master of Science, Faculdade de Engenharia da Universidade do Porto, Universidade do PortoOrtigueira, M.D., Tenreiro MacHado, J., Fractional signal processing and applications (2003) Signal Processing, 33, pp. 2285-2286Tenreiro MacHado, J., Kiryakova, V., Mainardi, F., Recent history of fractional calculus (2011) Nonlinear Sci. Num. Sim., 16, pp. 1140-1153Poinot, T., Trigeassou, J.-C., A method for modelling and simulation of fractional systems (2003) Signal Processing, 83, pp. 2319-2333Gabano, J.D., Poinot, T., Fractional modelling and identification of thermal systems (2011) Signal Processing, 91, pp. 531-541Lin, J., Point, T., Trigeassou, J.C., Coirault, P., Parameter estimation of fractional systems. Application to heat transfer (2001) ECC 2001, European Control Conference, pp. 2644-2649. , Porto, PortugalPoint, T., Trigeassou, J.C., Parameter estimation of fractional models application to the modeling of diffusive systems (2002) 15th IFAC World Congress, , Barcelona, SpainBenchellal, A., Point, T., Trigeassou, J.-C., Approximation and identification of diffusive interfaces by fractional models (2006) Signal Processing, 86, pp. 2712-272