Kiran M. Kolwankar, Anil D. Gangal Fractional differentiability of nowhere differentiable functions and dimensions (23K, gzipped uuencoded LaTeX) ABSTRACT. Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the `critical order' $2-s$ and not so for orders between $2-s$ and $1$, where $s$, $1