Foliation on Distribution with Finslerian Metric

A distribution $D$ with a admissible Finsler metric is defined on a smooth manifold $X$. Let $F$ be a foliation on $X$. On the distribution of $D$ as on a smooth manifold foliation $F$ corresponds to the foliation $TF$. Using this foliation and connection over distribution we define analog exterior derivative. Exterior differential forms is applied to a special form.