Two-point boundary value problems for finite fractional difference equations

By Ferhan Merdivenci Atici, Paul W. Eloe. 2011

262 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b4c49c144701fdd2a2e8fee53d7788dfb25d515a

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Systems of semipositone discrete fractional boundary value problems (2014, background): “, [9,25]), but we state them here for the sake of convenience.”
ON POSITIVE SOLUTIONS TO NONLOCAL FRACTIONAL AND INTEGER-ORDER DIFFERENCE EQUATIONS (2011, background): “3 extends the results in [6, 12, 21, 22, 23], among others.”
On a discrete fractional three-point boundary value problem (2012, background): “Very recently Atici and Eloe have produced several papers on the basic theory of discrete fractional initial value problems (IVPs) and boundary value problems (BVPs) – see, for example, 4-6 8 .”
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.”
A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity (2020, background): “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”
ANALYSIS OF DISCRETE FRACTIONAL OPERATORS (2015, methodology): “For this purpose we consider a forward fractional difference operator of Riemann-Liouville type as in the papers [2–7], We then prove some monotonicity criteria for a function f which is defined on N0 and has a sign (positive or negative) for ∆f when ν is between 0 and 1.”