الفهرس 
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Abstract
In last years, considerable attention has been focused in the so called fractional calculus, which allow us to consider integration and differentiation of any order not necessarily integer. The problem is old, known since 18th century, but also new with much interest in past 30 years. In the last decades besides theoretical research of fractional order derivatives and integrals, there are growing number of applications of the fractional order calculus in such different areas as e.g. long electrical lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, chaos, control theory and in many other areas.
Fractional order control system is a dynamic control system expressed by a differential equation where the order of the derivatives can take any real (sometimes complex) number, not necessary integer number.
The aim of this thesis is to study some structure properties of the linear control systems, the singular control systems and the discrete time control systems of fractional order in two cases; when the state and the control spaces are finite and infinite dimensional spaces. The structure properties of controllability, observability, set of reachability, domain of null controllability, stability and others, are of main interest for any dynamical control system either in the finite or in the infinite dimensional spaces.
So this work ties three mathematical subjects; control theory, fractional deferential equations and functional analysis.