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Fractional Clifford–Fourier Transform and its Application

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Abstract

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 transform in the form of integral. Then, we discuss the relationship between the FrCFT and the Clifford–Fourier transform (CFT) and give some properties of the 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.

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Acknowledgements

This work was supported by the National Science Foundation of China (no. 11871191) and the Natural Science Foundation of Hebei Province (A2020205008) and Hebei University of Science and Technology Dr. Fund (no. 1181348).

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Authors and Affiliations

  1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, Hebei, People’s Republic of China

    Haipan Shi & Yuying Qiao

  2. College of Science, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, People’s Republic of China

    Heju Yang & Zunfeng Li

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  1. Haipan Shi
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  2. Heju Yang
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  3. Zunfeng Li
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  4. Yuying Qiao
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Correspondence to Yuying Qiao.

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Communicated by Uwe Kaehler

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Shi, H., Yang, H., Li, Z. et al. Fractional Clifford–Fourier Transform and its Application. Adv. Appl. Clifford Algebras 30, 68 (2020). https://doi.org/10.1007/s00006-020-01094-4

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  • DOI: https://doi.org/10.1007/s00006-020-01094-4

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