Generalization of the modulating functions method into the fractional differential equations

摘要

The main aim of the paper is to generalize the modulating functions method to be useful in all models described by differential equations with fractional derivatives, if fractional differential operator is linear. The other aim is to prove that the task of parameter identification for differential equation with fractional differentials can be simplified or reduced to an integer order. The main role of modulating functions is to reduce the order of the derivative in the equation, to obtain equations without derivatives of the output signal and to eliminate the necessity of solving differential equations.