Exponential functions of discrete fractional calculus
By Nihan Acar, Ferhan Merdivenci Atici. 2013
73 citations recorded by the source corpus.
In this paper, exponential functions of discrete fractional calculus with the nabla operator are studied. We begin with proving some properties of exponential functions along with some relations to the discrete Mittag-Leffler functions. We then study sequential linear difference equations of fractional order with constant coefficients. A corresponding characteristic equation is defined and considered in two cases where characteristic real roots are same or distinct. We define a generalized Casoratian for a set of discrete functions. As a consequence, for solutions of sequential linear difference equations, their nonzero Casoratian ensures their linear independence.
View Paper: https://www.semanticscholar.org/paper/f784275601a33e6ec37595ef790836b30eea7a45
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Carlos Lizama
- Christopher S. Goodrich
- Ferhan Merdivenci Atici
- Meltem Uyanik
- Dorota Mozyrska
- Malgorzata Wyrwas
- Nihan Acar
- Baoguo Jia
Citations in the corpus
- A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity (2020, background): “In addition, many papers have provided an analysis of various abstract properties of discrete fractional operators—see, for example, the papers by Abdeljawad [5, 6], Anastassiou [9], Atici and Acar [10], Bastos, Mozyrska and Torres [18], Ferreira [23], Lizama [43], Lizama and Murillo-Arcila [45], an”
- ANALYSIS OF DISCRETE FRACTIONAL OPERATORS (2015, background): “For the convenience of the reader, we recall its definition (see [1, 2]).”
- The -Transform Method and Delta Type Fractional Difference Operators (2015, methodology): “In [25] the sequential discrete fractional equations with some particular convention of the fractional difference are solved using the kind of fractional nabla discrete Mittag-Leffler functions.”