In this paper, the fractional equations of the mass-spring-damper system with Caputo and Caputo–Fabrizio derivatives are presented. The physical units of the system are preserved by introducing an auxiliary parameter σ. The input of the resulting equations is a constant and periodic source; for the Caputo case, we obtain the analytical solution, and the resulting equations are given in terms of the Mittag–Leffler function; for the Caputo–Fabrizio approach, the numerical solutions are obtained by the numerical Laplace transform algorithm. Our results show that the mechanical components exhibit viscoelastic behaviors producing temporal fractality at different scales and demonstrate the existence of Entropy 2015, 17 6290 material heterogeneities in the mechanical components. The Markovian nature of the model is recovered when the order of the fractional derivatives is equal to one.

Acceleration of wound healing can be achieved with the use of wound dressings. Through the electrospinning technique, a polymeric scaffold composed of two layers was processed: a gelatin and polyvinylpyrrolidone layer with gentamicin, and a second layer of cellulose acetate. The conditions for the electrospinning process were standardized for voltage parameters, feed flow and the distance from the injector to the collector. Once the values of the main variables for the electrospinning were optimized, a three-hour processing time was established to allow the separation of the material from the collector. The obtained material was characterized by observations on scanning electron microscopy, Fourier transform infrared spectroscopy and thermal analysis; contact angle measurement was performed to evaluate wettability properties, and antibacterial activity against Pseudomonas aeruginosa and Staphylococcus aureus were evaluated using the Kirby–Bauer test. The obtained fibers that form the bi-layer scaffold present diameters from 100 to 300 nm. The scaffold presents chemical composition, thermal stability, wettability characteristics and antibacterial activity that fulfill the proposal from this study, based on obtaining a scaffold that could be used as a drug delivery vehicle and a wound dressing material.

We present an alternative representation of integer and fractional electrical elements in the Laplace domain for modeling electrochemical systems represented by equivalent electrical circuits. The fractional derivatives considered are of Caputo and Caputo-Fabrizio type. This representation includes distributed elements of the Cole model type. In addition to maintaining consistency in adjusted electrical parameters, a detailed methodology is proposed to build the equivalent circuits. Illustrative examples are given and the Nyquist and Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. The advantage of our representation appears according to the comparison between our model and models presented in the paper, which are not physically acceptable due to the dimensional incompatibility. The Markovian nature of the models is recovered when the order of the fractional derivatives is equal to 1.