  In the present paper, by extending some fractional calculus to the framework
of Cliffors analysis, new classes of wavelet functions are presented. Firstly,
some classes of monogenic polynomials are provided based on 2-parameters weight
functions which extend the classical Jacobi ones in the context of Clifford
analysis. The discovered polynomial sets are next applied to introduce new
wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules
have been proved. The main tool reposes on the extension of fractional
derivatives, fractional integrals and fractional Fourier transforms to Clifford
analysis.
