Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes distributed elements of the Cole model type. The Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. A numerical Laplace transform is used with respect to the simulation of the fractional differential equations. From the results shown in the analysis, we obtain the formula for the equivalent electrical circuit of a simple spectrum, such as that generated by a real sample of blood tissue, and the corresponding Nyquist diagrams. In addition to maintaining consistency in adjusted electrical parameters, the advantage of using fractional differential equations in the study of the impedance spectra is made clear in the analysis used to determine a compact formula for the equivalent electrical circuit, which includes the Cole model and a simple RC model as special cases.

In this work a fractional differential equation for the electrical RLC circuit is studied. The order of the derivative being considered is 0 < γ ≤ 1. To keep the dimensionality of the physical quantities R, L and C an auxiliary parameter γ is introduced. This parameter characterizes the existence of fractional components in the system. It is shown that there is a relation between and σ through the physical parameters RLC of the circuit. Due to this relation, the analytical solution is given in terms of the Mittag-Leffler function depending on the order of the fractional differential equation.

An alternative procedure to construct local supersymmetric quantum cosmological models is presented. This is performed by introducing a superfield formulation and is applied here to the FRW model. It has the advantage of being more simple than models proposed based on full supergravity and gives, by means of this local symmetry procedure, in a direct manner, the corresponding fermionic partners. It also permits the inclusion of matter in a systematic way. © 1996 The American Physical Society.

Making use of supersymmetry breaking selection rules under local n = 2 conformal supersymmetry we are able to obtain a normalizable wavefunction (at zero energy) of the universe for the FRW cosmological model (k = 0). For this purpose it is necessary to `weight' the inner product with the scalar factor R. The appropriate Hermitian operators are constructed and the expectation value of R is calculated giving us the size of the universe.