In this paper, we consider a version of the fractional Clifford-Fourier transform (FrCFT) and study its several properties and applications to partial differential equations in Clifford analysis. First, we give the definition of the FrCFT and its inverse definition in the form of integral. Then, we discuss the relationship between the FrCFT and the Clifford-Fourier transform (CFT) introduced by Hitzer et al (Theorem 3.3), and some properties of FrCFT, including Plancherel identity, differential properties, etc. Especially we give a new form of differential formula. Finally, we give an application of these results to a partial differential equation. Many researchers have done detailed research on the CFT. Brackx et al [1] defined Clifford-Fourier transform in the framework of Clifford analysis, as operator exponentials with a Clifford algebra-valued kernel. Hitzer and Bahri [2] defined a generalized real Fourier transform on Clifford multivector-valued functions and showed some properties of the CFT, including left linearity, vector differential, Plancherel theorem and so on. In terms of the FrCFT , De Bie and De Schepper [3] introduced a fractional version of the CFT depending on two numerical parameters and derived a series expansion for the kernel of the resulting integral transform. In the case of even dimension, an explicit expression for the kernel in terms of Bessel functions was also obtained. Based on the above work, Li et al [4] proved several versions of the real Paley-Wiener theorems for a FrCFT. Craddock and Hogan [5] solved appropriate wave-type problems on spheres in two and four dimensions and gave formulae for the solutions of these problems in all even dimensions and hence a means of computing the fractional Clifford-Fourier kernels in even dimensions. [1] Brackx F, De Schepper N, Sommen F. The Clifford-Fourier Transform. J Fourier Anal Appl 11, 669-681 (2005). [2] Hitzer E, Bahri M. Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n=2 (mod 4) and n=3 (mod 4). AACA 18, 715–736 (2008). [3] De Bie H, De Schepper N. The Fractional Clifford-Fourier Transform. Complex Anal. Oper., Theory 6: 1047 (2012). [4] Li S, Leng J, Fei M. Spectrums of Functions Associated to the Fractional Clifford–Fourier Transform. Adv. Appl. Clifford Algebras 30, 6 (2020). [5] Craddock M J, Hogan J A. The Fractional Clifford-Fourier Kernel. J. Fourier Anal. Appl., 19: 683 (2013).