A boundary value problem for a random-order fractional differential equation

In this paper, we define a new Riemann-Liouville fractional integral with random order, from this Caputo and Riemann-Liouville fractional derivatives are straightforward obtained, where the fractional order of these operators is a simple random variable. We derive useful properties analogous to those of the fractional operators with constant order, such as the semigroup property. As an application, we study a boundary value problem for the fractional oscillator with random order, using a random integral equation of Fredholm type. Finally, in order to solve this problem, we adapt the Nystrom method to get a numerical solution. (C) 2022 The Author(s). Published by Elsevier B.V.