On a Generic Fractional Derivative Associated with the Riemann–Liouville Fractional Integral
In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann–Liouville fractional integral. Then, the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied to deduce its properties. In particular, we characterize...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-09-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/13/9/604 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann–Liouville fractional integral. Then, the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied to deduce its properties. In particular, we characterize its domain, null-space, and projector operator; establish the interrelations between its different realizations; and present a generalized fractional Taylor formula involving the generic fractional derivative. Then, we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed-form formula for its unique solution, and study its complete monotonicity. |
|---|---|
| ISSN: | 2075-1680 |