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On Riesz Derivative

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Abstract

This paper focuses on studying Riesz derivative. An interesting investigation on properties of Riesz derivative in one dimension indicates that it is distinct from other fractional derivatives such as Riemann-Liouville derivative and Caputo derivative. In the existing literatures, Riesz derivative is commonly considered as a proxy for fractional Laplacian on ℝ. We show the equivalence between Riesz derivative and fractional Laplacian on ℝn with n ≥ 1 in details.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Min Cai & Changpin Li

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  1. Min Cai
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  2. Changpin Li
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Correspondence to Changpin Li.

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Cai, M., Li, C. On Riesz Derivative. FCAA 22, 287–301 (2019). https://doi.org/10.1515/fca-2019-0019

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  • DOI: https://doi.org/10.1515/fca-2019-0019

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