ABSTRACT In this work we identify the source in a 1D anomalous diffusion equation, from measurements of the concentration at a finite number of points. We use Caputo-Fabrizio time fractional derivative to model the phenomenon. Separating variables, we arrive to a linear system which provides approximate values for the Fourier coefficients of the unknown source. Numerical examples show the efficiency of the method, as well as some of its practical limitations.

We focus on the Forward Problem of electroencephalography, discuss a mathematical model and state properties of its weak solutions. A static and a time-dependent model for the source are considered. Numerical solutions, obtained by a Boundary Element Method technique, are compared with the analytical ones and with EEG recordings.

In this work we present an output feedback algorithm that solves the trajectory tracking problem in control affine nonlinear systems. This algorithm, is an improvement, for this class of systems, of that of (Mancilla Aguilar et al. 2000a), since it reduces the chattering effect on the control while keeping the original performance. In addition, and via a high gain observer, it deals with discrete output measurements instead of the states, as the original algorithm does.