Fractional Derivative Fractional Exponential Function Rabotnov's Hereditarity Elastic Medium 74D05 26A33
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 10, No 2, (2007), 111p-121p
In this paper, a comparative analysis of the models involving fractional
derivatives of di®erent orders is given. Such models of viscoelastic materials
are widely used in various problems of mechanics and rheology. Rabotnov's
hereditarily elastic rheological model is considered in detail. It is shown
that this model is equivalent to the rheological model involving fractional
derivatives in the stress and strain with the orders proportional to a certain
positive value less than unit. In the scienti¯c literature such a model is
referred to as Koeller's model. Inversion of Rabotnov's model developed
by himself based on algebra of operators results in similar rheological dependences.
Inversion of Koeller's model carried out using Miller's theorem
coincides inherently with Rabotnov's inversion procedure.