Random Fractional Hermite Differential Equation: A full study in mean square sense

Abstract

[EN] In this contribution a full probabilistic study for the Random Fractional Hermite differential equation is performed. Firstly, applying the random fractional Fr¿obenius method we will construct a solution convergent in mean square sense. Then, we will obtain reliable approximations for the mean and for the standard deviation taking into account that the solution described by a power series converges in mean square sense. After that, we will go a step further computing first probability density function of the solution. Finally, we show one numerical example to illustrate the theoretical findings.