scholarly journals Superconvergence Points for the Spectral Interpolation of Riesz Fractional Derivatives

2019 ◽  
Vol 81 (3) ◽  
pp. 1577-1601 ◽  
Author(s):  
Beichuan Deng ◽  
Zhimin Zhang ◽  
Xuan Zhao
Keyword(s):  
Fractional Derivatives ◽  
Riesz Fractional Derivatives ◽  
Spectral Interpolation

scholarly journals Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Vladimir Varlamov
Keyword(s):  
Fractional Derivatives ◽  
Full Range ◽  
Zeta Functions ◽  
Liouville Problem ◽  
Riesz Potentials ◽  
Hilbert Transforms ◽  
Riesz Fractional Derivatives ◽  
Linearly Independent ◽  
De Vries ◽  
Sturm Liouville

Riesz potentials (also called Riesz fractional derivatives) and their Hilbert transforms are computed for the Korteweg-de Vries soliton. They are expressed in terms of the full-range Hurwitz Zeta functions and . It is proved that these Riesz potentials and their Hilbert transforms are linearly independent solutions of a Sturm-Liouville problem. Various new properties are established for this family of functions. The fact that the Wronskian of the system is positive leads to a new inequality for the Hurwitz Zeta functions.

On Fractional Derivatives and Application

2013 ◽  
Vol 1 (2) ◽  
pp. 51-56
Author(s):  
Mark Borres ◽  
◽  
Efren Barabat ◽  
Jocelyn Panduyos ◽  
◽  
...  
Keyword(s):  
Fractional Derivatives
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