fractional integration
The basic idea of ”Riemann-Liouville” type fractional integration comes from the following observation:
Given any integrable function in one variable, we have the following Cauchy Integration Formula:
when switching the index from integer to non-integer gives the ideas of the following definitions:
Definition 1: Left-Hand Riemann-Liouville Integration
where
Definition 2: Right-Hand Riemann-Liouville Integration
where
Definition 3: Riesz Potential
where
,
for , for , for
and is the gamma function of
Title | fractional integration |
---|---|
Canonical name | FractionalIntegration |
Date of creation | 2013-03-22 16:17:47 |
Last modified on | 2013-03-22 16:17:47 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 17 |
Author | rspuzio (6075) |
Entry type | Definition |
Classification | msc 26A33 |
Synonym | fractional integral |