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Two nonlinear anelastic models with fractional derivatives, describing the properties of a series of materials as polymers, and polycrystalline materials are presented in this paper. These models are studied analytically, using a variational iteration method. The paper clarifies the different ways in which the fractional differentiation operator can be defined. A Volterra series method of model parameters identification from the experimental data is also presented.

ABSTRACT:The aim of this study is to establish a new representation for the dynamic algebra of the Morse oscillator and to establish the raising and lowering operators based on the properties of the confluent hypergeometric functions.Using the representation we have obtained a recurrent analytic method for the calculus of the Franck᎐Condon factors.

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The operator algebras of a new family of relativistic geometric models of the relativistic oscillator [1] are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the generators of a non-unitary representation of the so(1, 2) algebra, except a special case when this algebra becomes the standard one of the non-relativistic harmonic oscillator.Pacs: 04.62.+v, 03.65.Ge

This paper applies the Euler and the fourth-order Runge–Kutta methods in the analysis of fractional order dynamical systems. In order to illustrate the two techniques, the numerical algorithms are applied in the solution of several fractional attractors, namely the Lorenz, Duffing and Liu systems. The algorithms are implemented with the aid of Mathematica symbolic package. Furthermore, the Lyapunov exponent is obtained based on the Euler method and applied with the Lorenz fractional attractor.

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