In this paper, we introduce the fractional wavelet transformations (FrWT) involving Hankel–Clifford integral transformation (HClIT) on the positive half line and studied some of its basic properties. Also we obtain Parseval’s relation and an inversion formula. Examples of fractional powers of Hankel–Clifford integral transformation (FrHClIT) and FrWT are given. Then, we introduce the concept of fractional wavelet packet transformations FrBWPT and FrWPIT, and investigate their properties. © 2016, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.