Let for be defined its Riemann-Liouville fractional derivative by
and its Riemann-Liouville fractional integral by
The authors consider the fractional differential equations
and the fractional integral equation
driven by Lévy noise . The singularity spectrum of solution of (2) is obtained. They also study conditions under which this solution is a semi-martingale.
The authors give a numerical scheme to approximate the sample paths of equations of the form (1). This scheme is almost surely uniformly convergent. Using this numeric algorithm the authors present the sample paths of some fractional differential equation.