Some tools to study random fractional differential equations and applications

Differential equations with uncertainties and fractional derivatives are currently two cut-edge topics. The former have an important impact to deal with classical models whose input data must be treated as random quantities (random variables or stochastic processes) because, in practice, input data (coefficients, source term, initial and boundary conditions) must be often fixed after measurements then containing uncertainties. The latter are being particularly useful to model the dynamic of complex phenomena such as viscoelasticity, hysteresis, subdiffusion, etc. In this paper we present some results to deal with random fractional differential equations whose uncertainty can have quite general patterns. We will provide some theoretical results about mean square converge for these type of differential equations. Furthermore, we will showcase some methods to approximate the main statistical moments and the probability density function of the solution stochastic process to specific classes of random differential equations.