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

Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets