Remarks on the Generalized Fractional Laplacian Operator
Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada
Department of Mathematics, Shanghai University, Shanghai 200444, China
Author to whom correspondence should be addressed.
Received: 25 February 2019 / Revised: 21 March 2019 / Accepted: 25 March 2019 / Published: 29 March 2019
PDF [277 KB, uploaded 29 March 2019]
The fractional Laplacian, also known as the Riesz fractional derivative operator, describes an unusual diffusion process due to random displacements executed by jumpers that are able to walk to neighbouring or nearby sites, as well as perform excursions to remote sites by way of Lévy flights. The fractional Laplacian has many applications in the boundary behaviours of solutions to differential equations. The goal of this paper is to investigate the half-order Laplacian operator
in the distributional sense, based on the generalized convolution and Temple’s delta sequence. Several interesting examples related to the fractional Laplacian operator of order
are presented with applications to differential equations, some of which cannot be obtained in the classical sense by the standard definition of the fractional Laplacian via Fourier transform.
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MDPI and ACS Style
Li, C.; Li, C.; Humphries, T.; Plowman, H. Remarks on the Generalized Fractional Laplacian Operator. Mathematics 2019, 7, 320.
Li C, Li C, Humphries T, Plowman H. Remarks on the Generalized Fractional Laplacian Operator. Mathematics. 2019; 7(4):320.
Li, Chenkuan; Li, Changpin; Humphries, Thomas; Plowman, Hunter. 2019. "Remarks on the Generalized Fractional Laplacian Operator." Mathematics 7, no. 4: 320.
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