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.
Acknowledgements
The work was partially supported by the National Natural Science Foundation of China under Grant Nos. 11671251 and 11632008.
References
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© 2019 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–2–2019)
- Discussion Paper
- The flaw in the conformable calculus: It is conformable because it is not fractional
- The failure of certain fractional calculus operators in two physical models
- Research Paper
- Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative
- On Riesz derivative
- A note on fractional powers of strongly positive operators and their applications
- Semi-fractional diffusion equations
- Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
- Well-posedness of fractional degenerate differential equations in Banach spaces
- Structure factors for generalized grey Browinian motion
- Linear stationary fractional differential equations
- Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
- On fractional differential inclusions with Nonlocal boundary conditions
- On solutions of linear fractional differential equations and systems thereof
- Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses
- A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations
- On representation and interpretation of Fractional calculus and fractional order systems
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–2–2019)
- Discussion Paper
- The flaw in the conformable calculus: It is conformable because it is not fractional
- The failure of certain fractional calculus operators in two physical models
- Research Paper
- Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative
- On Riesz derivative
- A note on fractional powers of strongly positive operators and their applications
- Semi-fractional diffusion equations
- Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
- Well-posedness of fractional degenerate differential equations in Banach spaces
- Structure factors for generalized grey Browinian motion
- Linear stationary fractional differential equations
- Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
- On fractional differential inclusions with Nonlocal boundary conditions
- On solutions of linear fractional differential equations and systems thereof
- Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses
- A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations
- On representation and interpretation of Fractional calculus and fractional order systems