  In this work, a new relationship is established between the solutions of
higher fractional differential equations and a Wright-type transformation.
Solutions could be interpreted as expected values of functions in a random time
process. As applications, we solve the fractional beam equation, fractional
electric circuits with special functions as external sources, and derive
dAlemberts formula for the fractional wave equation. Due to this relationship,
we present two methods for simulating solutions of fractional differential
equations. The two approaches use the interpretation of the Caputo derivative
of a function as a Wright-type transformation of the higher derivative of the
function. In the first approach, we use the Runge-Kutta method of hybrid orders
4 and 5 to solve ordinary differential equations combined with the Monte Carlo
integration to conduct the Wrighttype transformation. The second method uses a
feedforward neural network to simulate the fractional differential equation.
