This paper presents a method for including initial conditions in recursive constant and variable fractional-order derivatives. The initial conditions are assumed to be in the form of a time-constant function. The numerical scheme for solving fractional-order differential equations, given in the matrix form, is presented as well. Results obtained with the proposed numerical algorithm are compared with the analog realization of a fractional-order inertial system. For the constant-order case, analog models were built based on domino ladder approximations for 0.5 and 0.25 orders. For the variable-order case, the analog model was built based on the reductive-switching structure. Comparison with the physical systems shows the ability of the proposed method to describe the behavior of real fractional-order systems with initial conditions.
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