By Krzysztof J. Latawiec, Marian Łukaniszyn, Rafal Stanislawski

This quantity provides chosen facets of non-integer, or fractional order platforms, whose research, synthesis and functions have more and more turn into a true problem for numerous learn groups, starting from technological know-how to engineering. The spectrum of purposes of the fractional order calculus has particularly improved, actually it might be demanding to discover a science/engineering-related topic quarter the place the fractional calculus had now not been integrated. The content material of the fractional calculus is ranged from natural arithmetic to engineering implementations and so is the content material of this quantity. the quantity is subdivided into six elements, reflecting specific facets of the fractional order calculus. the 1st half incorporates a unmarried invited paper on a brand new formula of fractional-order descriptor observers for fractional-order descriptor continous LTI structures. the second one half presents new components to the mathematical thought of fractional-order platforms. within the 3rd a part of this quantity, a host of latest leads to approximation, modeling and simulations of fractional-order structures is given. The fourth half offers new ideas to a few difficulties in controllability and keep an eye on of non-integer order structures, particularly fractional PID-like keep watch over. The 5th half analyzes the steadiness of non-integer order platforms and a few new effects are provided during this very important admire, specifically for discrete-time structures. the ultimate, 6th a part of this quantity offers a spectrum of functions of the noninteger order calculus, starting from bi-fractional filtering, particularly of electromyographic indications, during the thermal diffusion and advection diffusion techniques to the SIEMENS platform implementation. This volume's papers have been all subjected to stimulating reviews and discussions from the energetic viewers of the RRNR'2014, the sixth convention on Non-integer Order Calculus and Its functions that was once geared up through the dep. of electric, keep an eye on and laptop Engineering, Opole collage of know-how, Opole, Poland.

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**Extra info for Advances in Modelling and Control of Non-integer-Order Systems: 6th Conference on Non-integer Order Calculus and Its Applications, 2014 Opole, Poland**

**Sample text**

These identities Noether called “dependencies”. For example, the Bianchi identities, in the general theory of relativity, are examples of such “dependencies”. J. Latawiec et al. B. Malinowska and T. Odzijewicz chromodynamics and other gauge ﬁeld theories. It should be mentioned that a generalize of the second Noether theorem to fractional problems was already proved in [10]. However, in contrast with this work, where fractional operators with a constant non-integer order α were considered, here we study more general fractional variational problems with variable order derivatives.

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Regular fractional Sturm-Liouville problem with discrete spectrum: solutions and applications. In: Proceedings of the 2014 International Conference on Fractional Diﬀerentiaton and Its Applications, Catania, Italy, June 23-25 (2014) 13. : Existence of positive solutions for Sturm–Liouville BVPs of singular fractional diﬀerential equations. U. P. B. Sci. Bull. Series A, 74 (2012) 14. : Fractional Pearson diﬀusion. J. Math Anal. Appl. 403, 532–546 (2013) 15. : Introduction to the Fractional Calculus of Variations.