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In this paper we present a new method for the construction of strongsolutions of SDE's with merely integrable drift coefficients driven by amultidimensional fractional Brownian motion with Hurst parameter H < 1/2.Furthermore, we prove the rather surprising result of the higher order Frechetdifferentiability of stochastic flows of such SDE's in the case of a smallHurst parameter. In establishing these results we use techniques from Malliavincalculus combined with new ideas based on a "local time variational calculus".We expect that our general approach can be also applied to the study of certaintypes of stochastic partial differential equations as e.g. stochasticconservation laws driven by rough paths.

Strong existence and higher order Fr\'echet differentiability of stochastic flows of fractional Brownian motion driven SDE's with singular drift