Introduce students to basic concepts of fractional calculus. It is possible to solve problem of modeling as well as control task of the fractional order system (FOS) using modern theory based on fractional calculus. Determination (simulation) models of FOS - i.e. fractional differential equations of motion of the FOS, as well as fractional order controls which are important in practical problems of the FOS.Practical simulations FOS using MATLAB software package.

By attending this course student acquires the ability to analyze problems and synthesis solutions to the problem of modeling and control of given fractional order systems using scientific methods of fractional calculus. This enabled him applying solutions to practical problems of fractional order systems as well as monitoring and implementation of innovation of new results of fractional calculus.

Basic definitions and properties of fractional derivatives and integrals. Cauchy type problem for ordinary fractional linear equations. Fractional existence and uniqueness theorems. Equations with the Riemann-Liouville fractional derivative. Equations with the Caputo derivatives in the space of continuous differentiable functions. Laplace transform method for solving ordinary differential equations with R-Liouville fractional derivatives.Laplace transform method for solving ordinary differential equations with Caputo fractional derivatives.Solution of Cauchy type problems for given fractional equations. Fractional order control.Numerical methods for fractional order systems.Applications with MATLAB for given fractional order system-examples in engineering.

Applications MATLAB for given fractional order systemс -examples in engineering.

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1.M.Lazarević, Lj.Bučanović, Contribution to modelling and dinamical analysis of fractional order system with fundamentals of fractional calculus 2.Podlubny I. Fractional Differential Equations. Academic Press, San Diego,1999 3.Kilbas, Srivastava, H.M., Trujillo, J.J.Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam,2006. 4.Hilfer R, Ed., Applications of Fractional Calculus in Physics,World Scientific, River Edge, NJ, USA, 2000. 5.AV Pskhu, AP Soldatov, Partial differential equations of fractional order, Nauka, Moscow, 2005 6.Written abstracts from the lectures (Handouts) 7.MATLAB,MATHEMATICA-mathematics software packages

Total assigned hours: 65

New material: 30
Elaboration and examples (recapitulation): 20

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 5
Review and grading of seminar papers: 5
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 50
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 30

Oldham K B and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, Dover Publication, 2006. ; C. A. Monje, YQ. Chen, B. M. Vinagre, D. Xue, V. Feliu, Fractiona Order Systems and Controls – Fundamentals and Applications, Springer, 2010; K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Willey & Sons, Inc. 1993; R. Magin. Fractional Calculus in Bioengineering. Begell House, Inc. 2006; J.Sabatier,O Agrawal,J.Machado,ADVANCES IN FRACTIONAL CALCULUS,Springer,Netherlands,2007.