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Journal of Applied Nonlinear Dynamics 6(2) (2017) 131--134 | DOI:10.5890/JAND.2017.06.001

Cristina I. Muresan, Piotr Ostalczyk$^{2}$, Manuel D. Ortigueira$^{3}$

$^{1}$ Department of Automation, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Memorandumului Street, no 28, 400114 Cluj-Napoca, Romania

$^{2}$ Institute of Applied Computer Science, Lodz University of Technology, 90-924 Lodz, Poland

$^{3}$ UNINOVA and DEE/ Faculdade de Ciˆencias e Tecnologia da UNL, Campus da FCT, Quinta da Torre,2829-516 Caparica, Portugal

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Abstract

Fractional calculus represents the generalization of integration and differentiation to an arbitrary order. Since the very first occurrence of fractional differentiation more than 300 years ago, fractional calculus and research related to its possible application have deserved ever-growing attention and interest. The research community has managed to bring forward ideas and concepts that justify the importance of fractional calculus for future engineering and science discoveries. What has begun as a means to describe abnormal behaviours in viscoelasticity or diffusion, power law phenomena, long range processes or fractal structures has spread to almost all engineering fields and applied sciences. Nowadays, its use in control engineering has been gaining more and more popularity in both modeling and identification, as well as in the controller tuning.

References

1. [1]	Pacheco, C., Duarte-Mermoud, M.A., Aguila-Camacho, N., and Castro-Linares, R. (2017), Fractional-order state observers for integer-order linear systems, Journal of Applied Nonlinear Dynamics, 6(2), 251-264.

2. [2]	Bento, T. Valerio, D., Teodoro, P., and Martins, J. (2017), Fractional order image processing of medical images, Journal of Applied Nonlinear Dynamics, 6(2), 181-191.

3. [3]	Yüce, A. and Tan, N. (2017), Derivation of analytical inverse Laplace transform for fractional order integrator, Journal of Applied Nonlinear Dynamics, 6(2), 303-314.

4. [4]	Markowski, K. A. (2017), Two cases of digraph structures corresponding to minimal positive realisation of fractional continuous-time linear systems, Journal of Applied Nonlinear Dynamics, 6(2), 265-282.

5. [5]	Adams, J. L., Veillette, R. J., and Hartley, T.T. (2017), A method for the Hankel-Norm approximation of fractional-order systems, Journal of Applied Nonlinear Dynamics, 6(2), 153-171.

6. [6]	Le Méhauté, A. and Riot, P. (2017), Arrows of times, non integer operators, self-similar structures, zeta functions and Riemann hypothesis: a synthetic categorical approach, Journal of Applied Nonlinear Dynamics, 6(2), 283-301.

7. [7]	Hartley, T.T (2017), Voltage synchronization in an array of fractional-order energy storage elements, Journal of Applied Nonlinear Dynamics, 6(2), 193-223.

8. [8]	Milici, C. and Draganescu, Gh. (2017), The Lane - Emden fractional homogeneous differential equation, Journal of Applied Nonlinear Dynamics, 6(2), 237-242.

9. [9]	Milici, C. and Draganescu, Gh. (2017), Generalization of the equations of Hermite, Legendre and Bessel for the fractional case, Journal of Applied Nonlinear Dynamics, 6(2), 243-249.

10. [10]	Zhokh, A. A. and Strizhak, P.E. (2017), Experimental verification of the time-fractional diffusion of methanol in silica, Journal of Applied Nonlinear Dynamics, 6(2), 135-151.

11. [11]	Abdel-Rehim, E. A. and Brikaa, M.G. (2017), Quadratic spline function for the approximate solution of an intermediate space-fractional advection diffusion equation, Journal of Applied Nonlinear Dynamics, 6(2), 225-236.

12. [12]	Cernea, A. (2017), On the solutions of some boundary value problems for integro-differential inclusions of fractional order, Journal of Applied Nonlinear Dynamics, 6(2), 173-179.