Before revision:  Our theoretical results naturally suggest a numerical algorithm to explicitly obtain the solution to quadratic ordinary differential equations of fractional type, that turns out to be quite promising in terms of computational performance. In particular, we introduce a hybrid numerical scheme, we test its precision by comparing our results with the (few) benchmark available in the literature, based on the Adams method , and we numerically study the convergence of our procedure .
After revision:  Our theoretical results naturally suggest a numerical algorithm to explicitly obtain the solution to quadratic ordinary differential equations of fractional type, that turns out to be extremely fast and stable. When applied to option pricing, our method largely outperforms the only available alternative in the literature, based on the Adams method , and we numerically study the convergence of our procedure .