| Title:
|
Nonoscillatory solutions of discrete fractional order equations with positive and negative terms (English) |
| Author:
|
Alzabut, Jehad |
| Author:
|
Grace, Said Rezk |
| Author:
|
Selvam, A. George Maria |
| Author:
|
Janagaraj, Rajendran |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
461-479 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper aims at discussing asymptotic behaviour of nonoscillatory solutions of the forced fractional difference equations of the form \begin{align} \Delta ^{\gamma }u(\kappa )&+\Theta [\kappa +\gamma ,w(\kappa +\gamma )]\\=&\Phi (\kappa +\gamma )+\Upsilon (\kappa +\gamma )w^{\nu }(\kappa +\gamma ) +\Psi [\kappa +\gamma ,w(\kappa +\gamma )],\quad \kappa \in \mathbb {N}_{1-\gamma },\\ u_{0} =&c_{0}, \end{align} where $\mathbb {N}_{1-\gamma }=\{1-\gamma ,2-\gamma ,3-\gamma ,\cdots \}$, $0<\gamma \leq 1$, $\Delta ^{\gamma }$ is a Caputo-like fractional difference operator. Three cases are investigated by using some salient features of discrete fractional calculus and mathematical inequalities. Examples are presented to illustrate the validity of the theoretical results. (English) |
| Keyword:
|
fractional difference equation |
| Keyword:
|
nonoscillatory |
| Keyword:
|
Caputo fractional difference |
| Keyword:
|
forcing term |
| MSC:
|
26A33 |
| MSC:
|
39A10 |
| MSC:
|
39A13 |
| MSC:
|
39A21 |
| idZBL:
|
Zbl 07790597 |
| idMR:
|
MR4673831 |
| DOI:
|
10.21136/MB.2022.0157-21 |
| . |
| Date available:
|
2023-11-23T12:34:39Z |
| Last updated:
|
2024-12-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151968 |
| . |
| Reference:
|
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