The Theory of Discrete Fractional Calculus: Development and Application

By Michael T. Holm. 2011

117 citations recorded by the source corpus.

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Citations in the corpus

Discrete chaos in fractional delayed logistic maps (2015, background): “After that, several authors developed the theory of the fractional difference equations on time scales [9], such as the initial value problems [10], the discrete calculus of variations [11], the Laplace transform [12,13], the properties of the Caputo and the Riemann-Liouville difference [14], and so”
On the asymptotic stability of linear system of fractional-order difference equations (2013, methodology): “Although a Riemann-Liouville-like definition is possible (see, for instance, [9, 13, 16]), we choose to define fractional differences in the Caputo sense because the constants will have zero fractional difference, among other properties.”
Some further results of the laplace transform for variable–order fractional difference equations (2019, methodology): “([10]) Suppose x: Na → R is of exponential order r ≥ 1 and let ν be given with m− 1 < ν ≤ m.”
Convexity for nabla and delta fractional differences (2015, methodology): “We next apply the following lemma (the Fractional Difference Power Rule), which appears in [13], [14] and [10].”
The Poisson distribution, abstract fractional difference equations, and stability (2017, methodology): “Holm [29, 30] further developed and applied the tools of discrete fractional calculus to the arena of fractional difference equations.”
lp ‐maximal regularity for fractional difference equations on UMD spaces (2015, methodology): “Holm [33], [34] further developed and applied the tools of discrete fractional calculus to the arena of fractional difference equations.”