I enjoyed your talk at the conference. I get the impression that jets on supermanifolds, or graded manifolds as I think you prefer to call them, is something that is not generally well understood. You might be interested in my publication ''On curves and jets of curves on supermanifolds'' where I go to some lengths to construct higher tangent bundles. Anyway, thanks for speaking at the conference.
Dear Professor Bruce thank you for the comment. I have seen your "Higher order mechanics on graded bundles" as like as its underlying publication arXiv: 1412.2719. I also keep in mind your very interesting publication arXiv: 1401.5267 that you mention. Thank you. The Conference really was very strong both by science and organization.