ANALYSIS OF DISCRETE FRACTIONAL OPERATORS

By Ferhan Merdivenci Atici, Meltem Uyanik. 2015

73 citations recorded by the source corpus.

In this paper, we introduce two new monotonicity concepts for a nonnegative or nonpositive valued function defined on a discrete domain. We give examples to illustrate connections between these new monotonicity concepts and the traditional ones. We then prove some monotonicity criteria based on the sign of the fractional difference operator of a function f, Δνf with 0 < ν < 1. As an application, we state and prove the mean value theorem on discrete fractional calculus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/49993f7ef9ac8804fdf6fe6aba0857110531eb8d

How researchers see this paper

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

In Applied Mathematics

1. Christopher S. Goodrich
2. Carlos Lizama
3. Nihan Acar
4. Ferhan Merdivenci Atici
5. Gaston M. N'Guérékata
6. Chuang Chen
7. Miao Li
8. Rodrigo Ponce

In Modeling and Simulation

1. Carlos Lizama
2. Christopher S. Goodrich
3. Nihan Acar
4. Ferhan Merdivenci Atici
5. Baoguo Jia
6. Lynn Erbe
7. Allan Peterson
8. Rajendra Dahal

In Numerical Analysis

1. Carlos Lizama
2. Christopher S. Goodrich
3. Ferhan Merdivenci Atici
4. Nihan Acar

Citations in the corpus

• A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity (2020, background): “More specifically, in recent papers by Atici and Uyanik [14], Baoguo et al. [16, 17], Dahal and Goodrich [19, 20, 21], Goodrich [26, 29, 30, 31, 32], and Jia et al. [38, 39] various connections between the sign of an appropriate discrete fractional operator, the corresponding monotonicity and convex”