  A parallel numerical simulation algorithm is presented for fractional-order
systems involving Caputo-type derivatives, based on the Adams-Bashforth-Moulton
(ABM) predictor-corrector scheme. The parallel algorithm is implemented using
several different approaches: a pure MPI version, a combination of MPI with
OpenMP optimization and a memory saving speedup approach. All tests run on a
BlueGene/P cluster, and comparative improvement results for the running time
are provided. As an applied experiment, the solutions of a fractional-order
version of a system describing a forced series LCR circuit are numerically
computed, depicting cascades of period-doubling bifurcations which lead to the
onset of chaotic behavior.
