Mittag-Leffler Functions
By Kai Diethelm. 2010
385 citations recorded by the source corpus.
Subfields: Signal Processing
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Signal Processing
- Tenreiro Machado
- J. Sousa
- Maione Guido
- G. Em Karniadakis
- Roberto Garrappa
- Lu Lu
- Rudolf Gorenflo
- Virginia S. Kiryakova
Citations in the corpus
- fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “The analytical forms of the space-fractional and the time-fractional derivatives of the fabricated solutions are given in [8] and [12], respectively.”
- Numerical solution of time fractional diffusion systems (2017, background): “j=0 z Γ(1 + αj) is the Mittag Leffler (ML) function and Γ is the gamma function, see the monograph [24] and survey [16] on the properties of generalised ML functions.”
- Time-fractional diffusion equation in the fractional Sobolev spaces (2015, background): “in the monographs [5], [13], [10], and [23].”
- On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the $$\psi $$ψ-Hilfer operator (2017, methodology): “[27] (One parameter Mittag-Leffler function).”
- Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, result): “We have taken the present occasion, as a compliment to our previous survey [107], to cite books published during the years 2011 [92, 80, 44, 26, 65, 47, 5, 106, 117], 2012 [7, 3, 77, 1, 51, 38, 102, 56, 122, 15, 112, 110, 118], 2013 [14, 18, 89, 29, 36], and 2014 [57, 4, 121, 39, 105, 40, 66, 86, 2,”
- A new truncated $M$-fractional derivative type unifying some fractional derivative types with classical properties (2017, background): “In 2017, Sousa and Oliveira [9], introduced an M -fractional derivative involving a Mittag-Leffler function with one parameter [10] that also satisfies the properties of integer-order calculus.”
- Models of dielectric relaxation based on completely monotone functions (2016, methodology): “Important results on the asymptotic behaviour of the standard (one or two parameter) ML function are largely available in the literature (see, for instance, [35, 47, 79, 80, 96]).”