Abstract
Supersingular integrals arise in many areas of applied mathematics: Fluid dynamics and fracture mechanics are among the most important ones. This paper is devoted to investigating the relationship between Riesz, Riesz-Caputo, Hilfer fractional derivatives and the corresponding finite part integrals in Hadamard sense. We prove that Riesz, Riesz-Caputo, and Hilfer derivatives of a given function can be expressed by the finite part integrals of a supersingular integrals which do not exist.
| Original language | English |
|---|---|
| Article number | 1950078 |
| Journal | Fractals |
| Volume | 27 |
| Issue number | 5 |
| DOIs | |
| State | Published - 1 Aug 2019 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019 World Scientific Publishing Company.
Keywords
- Finite Part Integral
- Fractional Derivative
- Hilfer Derivative
- Riesz Derivative
- Supersingular
ASJC Scopus subject areas
- Modeling and Simulation
- Geometry and Topology
- Applied Mathematics