Initial conditions for a recursive constant and variable fractional-order derivative and its verification based on analog model

The paper presents a method for including initial conditions into the recursive constant and variable fractional-order derivative definition. The initial conditions are assumed to be in the form of time constant function. Results obtained with proposed numerical algorithm are compared with analog realization of fractional order inertial system. For constant orders analog models were built based on domino ladder approximations for 0.5 and 0.25 orders. For variable order analog model the reductive-switching structure and the same domino ladder approximations were used. Comparison to the physical systems, presents ability of proposed method for describing behavior of real fractional order systems with initial conditions.