On the initial conditions in continuous-time fractional linear systems
Signal Processing - Special issue: Fractional signal processing and applications
A method for modelling and simulation of fractional systems
Signal Processing - Special issue: Fractional signal processing and applications
State variables and transients of fractional order differential systems
Computers & Mathematics with Applications
The infinite state approach: Origin and necessity
Computers & Mathematics with Applications
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Mastery of the initial conditions of fractional order systems remains an open problem, in spite of a great number of contributions. This paper proposes a solution dedicated to linear fractional differential equations (FDEs), which is based on an equivalence principle between the original system and an exactly equivalent infinite dimensional ordinary differential equation (ODE). This equivalence principle is derived from the fractional integration operator concept and the frequency distributed state space model of this operator. Thanks to this principle, the FDE initial conditions problem is converted into a conventional ODE initialization problem, however with an infinite dimensional state vector. Practical FDE initialization is performed using an observer based technique applied to the equivalent ODE; a numerical example demonstrates the efficiency of this approach.