Key points are not available for this paper at this time.
Bertram Ross, Stefan G. Samko, E. Russel Love, FUNCTIONS THAT HAVE NO FIRST ORDER DERIVATIVE MIGHT HAVE FRACTIONAL DERIVATIVES OF ALL ORDERS LESS THAN ONE, Real Analysis Exchange, Vol. 20, No. 1 (1994-95), pp. 140-157
Ross et al. (Sat,) studied this question.