Carla M.A. Pinto
Polytechnic of Porto, Portugal
Joint work with: C. Burgos, J.-C. Cortés, E. López-Navarro, and Rafael-J. Villanueva
Abstract: In Classical Mechanics, several problems are formulated by means of the differential equation y’’(t) + Atβ y(t) = 0. In this talk, we will show updates on recent results established for a randomized reformulation of this model that includes a non-integer order derivative. The stochastic analysis permits solving that model by computing reliable approximations of the probability density function of the solution, which is a stochastic process. The approach avoids constructing these approximations from limited statistical punctual information and the Principle of Maximum Entropy by directly constructing a sequence of approximations using the Probabilistic Transformation Method. We prove that these approximations converge to the exact density under mild conditions on the data. Finally, several numerical examples illustrate our theoretical findings.