Grünwald–Letnikov derivative
E898517
The Grünwald–Letnikov derivative is a fundamental definition of fractional differentiation based on limit processes and finite differences, widely used as a foundation for fractional calculus.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
fractional derivative definition
ⓘ
mathematical concept ⓘ notion in fractional calculus ⓘ |
| alternativeName | Grünwald–Letnikov fractional derivative NERFINISHED ⓘ |
| approximatedBy | fractional finite difference schemes ⓘ |
| basedOn |
finite differences
ⓘ
limit process ⓘ |
| category | nonlocal derivative ⓘ |
| characterizedBy | limit of fractional difference quotients ⓘ |
| defines | fractional order derivative ⓘ |
| domain |
complex-valued functions
ⓘ
real-valued functions ⓘ |
| equivalentTo | Riemann–Liouville derivative under suitable conditions ⓘ |
| field | fractional calculus ⓘ |
| generalizes | integer order derivative ⓘ |
| hasKernel | power-law type weighting ⓘ |
| hasRepresentation | infinite series ⓘ |
| hasType |
left-sided fractional derivative
ⓘ
right-sided fractional derivative ⓘ |
| introducedIn | 19th century ⓘ |
| mathematicalDiscipline |
analysis
ⓘ
operator theory ⓘ |
| namedAfter |
Aleksandr Letnikov
NERFINISHED
ⓘ
Alfred Grünwald NERFINISHED ⓘ |
| order |
complex order
ⓘ
real order ⓘ |
| property |
depends on function history
ⓘ
reduces to classical derivative when order is integer ⓘ |
| relatedTo |
Caputo derivative
NERFINISHED
ⓘ
Riemann–Liouville derivative NERFINISHED ⓘ fractional difference operator ⓘ fractional integral ⓘ |
| specialCaseOf | fractional difference calculus ⓘ |
| timeDomain | nonlocal operator ⓘ |
| usedFor |
modeling hereditary phenomena
ⓘ
modeling memory effects ⓘ |
| usedIn |
anomalous diffusion modeling
ⓘ
control theory ⓘ discrete-time fractional systems ⓘ fractional-order dynamical systems ⓘ numerical methods for fractional differential equations ⓘ signal processing ⓘ viscoelasticity modeling ⓘ |
| uses |
backward difference operator
ⓘ
binomial coefficients ⓘ discrete convolution sum ⓘ fractional order α ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.