Fractional differentiability of nowhere differentiable functions and dimensions
Fractional differentiability of nowhere differentiable functions and dimensions
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<s<2 is the box dimension of the graph of the function. This observation is consolidated …