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This paper is concerned with the investigation of the controllability andobservability of Caputo fractional differential linear systems of any realorder {\alpha} . Expressions for the expansions of the evolution operators inpowers of the matrix of dynamics are first obtained. Sets of linearlyindependent continuous functions or matrix functions, which are also Chebyshevsystems, appear in such expansions in a natural way. Based on the properties ofsuch functions, the controllability and observability of the Caputo fractionaldifferential system of real order {\alpha} are discussed as related to theircounterpart properties in the corresponding standard system defined for{\alpha} = 1. Extensions are given to the fulfilment of those properties undernon- uniform sampling. It is proved that the choice of the appropriate samplinginstants ion not restrictive as a result of the properties of the associateChebyshev systems

On Chebyshev systems and non-uniform sampling related to controllability and observability of caputo fractional differential systems