A transform method in discrete fractional calculus

By Ferhan Merdivenci Atici, Paul W. Eloe. 2007

499 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d208b8831c409e73a16c2375a83d3433fa54fa72

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

On Delta and Nabla Caputo Fractional Differences and Dual Identities (2011, background): “After then, several authors started to deal with discrete fractional calculus [1, 3, 4, 5, 6, 14, 12, 20, 21, 22, 27, 28], benefiting from time scales calculus originated in 1988 (see [15]).”
A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity (2020, methodology): “By contrast, a fractional forward difference of order α > 0 may be defined by (see Gray and Zhang [35] or Atici and Eloe [11, 12, 13]) (1.1) (∆νaf)(t) := 1 Γ(−ν) t+ν∑ s=a (t− s− 1)−ν−1f(s), t ∈ Na+N−ν , where N ∈ N1 is the unique integer satisfying N − 1 ν N , and the map t 7→ tν is defined by t”
The Poisson distribution, abstract fractional difference equations, and stability (2017, methodology): “The remarkable fact is that we use here a particular choice of the definition introduced by Atici and Eloe in [9] for the nabla operator.”
SOLUTIONS TO A DISCRETE RIGHT-FOCAL FRACTIONAL BOUNDARY VALUE PROBLEM (2010, background): “These and other related results and their proofs can be found, for example, in [3–6].”
Existence and uniqueness of solution to some discrete fractional boundary value problems of order less than one (2013, background): “It took almost 20 years for researchers to start developing this theory [2,3] but now authors are expanding this field of science in various directions [6,8,14,15].”
lp ‐maximal regularity for fractional difference equations on UMD spaces (2015, methodology): “Remark 2.6 The following definition of fractional sum was proposed by Atici and Eloe [10] in 2009: Let α > 0.”
DISCRETE FRACTIONAL CALCULUS WITH THE NABLA OPERATOR (2009, methodology): “For the readers’ benefit, we shall recall definitions of the fractional sum and ∆ difference operators, see [2, 4, 15].”