On Riesz derivative

By Minhao Cai, Changpin Li. Fractional Calculus and Applied Analysis, 2019

81 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/132e02814120d0f51ca70743df14070d9ae8c38e

Citations in the corpus

• Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results (2021, unknown): “The fractional-diffraction operator with the Lévy index α (in the original fractional Schrödinger equation, it characterizes the hopping motion of the quantum particle [9]) is defined, in the form of the Riesz derivative [45], by means of the juxtaposition of the direct and inverse Fourier transform”