By Krzysztof J. Latawiec, Marian Łukaniszyn, Rafal Stanislawski
This quantity offers chosen elements of non-integer, or fractional order structures, whose research, synthesis and functions have more and more turn into a true problem for numerous study groups, starting from technology to engineering. The spectrum of purposes of the fractional order calculus has tremendously accelerated, in truth it might be challenging to discover a science/engineering-related topic quarter the place the fractional calculus had now not been included. 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 components, reflecting specific elements of the fractional order calculus. the 1st half features 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 number of recent leads to approximation, modeling and simulations of fractional-order platforms is given. The fourth half provides new ideas to a couple difficulties in controllability and keep watch over of non-integer order platforms, particularly fractional PID-like keep an eye on. The 5th half analyzes the steadiness of non-integer order structures and a few new effects are provided during this very important appreciate, particularly for discrete-time platforms. the ultimate, 6th a part of this quantity provides a spectrum of purposes of the noninteger order calculus, starting from bi-fractional filtering, particularly of electromyographic indications, throughout the thermal diffusion and advection diffusion tactics 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 dept of electric, regulate and laptop Engineering, Opole college of expertise, Opole, Poland.
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Extra resources for Advances in Modelling and Control of Non-integer-Order Systems: 6th Conference on Non-integer Order Calculus and Its Applications, 2014 Opole, Poland
Fractional Pearson diﬀusion. J. Math Anal. Appl. 403, 532–546 (2013) 15. : Introduction to the Fractional Calculus of Variations. Imperial College Press, London (2012) 16. : Introducing an Iterative Method for Solving a Special FDE. International Mathematical Forum 4, 1449– 1456 (2009) 17. : From Sturm–Liouville problems to fractional and anomalous diﬀusions. Stochastic Processes and their Applications 122, 3513–3544 (2012) 18. : Fractional diﬀerential equations. Academic Press, San Diego (1999) 19.
Blasik version of SLPs yields solutions which correspond to real eigenvalues and are orthogonal eigenfunctions. The aim of this paper is to propose a simple method of proof of the existence result for a discrete spectrum of a regular FSLP with vanishing Dirichlet and fractional Neumann boundary conditions. We extend here an approach developed in  in the case of a regular FSLP with derivatives in the range (0,1). By using the methods of functional analysis we also prove that the respective inﬁnite countable set of eigenfunctions yields a basis in the space of square-integrable functions.
Birkh¨ auser Verlag (2013) 16. : Noether’s theorem for fractional variational problems of variable order. Cent. Eur. J. Phys. 11, 691–701 (2013) 17. : Variable order modeling of diﬀusive-convective eﬀects on the oscillatory ﬂow past a sphere. J. Vib. Control 14, 1569–1672 (2008) 18. : On the selection and meaning of variable order operators for dynamic modeling. Int. J. Diﬀer. Equ. 2010, 16, Art. ID 846107 (2010) 19. : On the variable order dynamics of the nonlinear wake caused by a sedimenting particle.