Nonoscillatory solutions of discrete fractional order equations with positive and negative terms
This paper aims at discussing asymptotic behaviour of nonoscillatory solutions of the forced fractional difference equations of the form \align\Delta^{\gamma}u(\kappa)&+\Theta[\kappa+\gamma,w(\kappa+\gamma)] =&\Phi(\kappa+\gamma)+\Upsilon(\kappa+\gamma)w^{\nu}(\kappa+\gamma) +\Psi[\kapp...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2023-12-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/148/4/mb148_4_3.pdf |
| _version_ | 1827696813403013120 |
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| author | Jehad Alzabut Said Rezk Grace A. George Maria Selvam Rajendran Janagaraj |
| author_facet | Jehad Alzabut Said Rezk Grace A. George Maria Selvam Rajendran Janagaraj |
| author_sort | Jehad Alzabut |
| collection | DOAJ |
| description | This paper aims at discussing asymptotic behaviour of nonoscillatory solutions of the forced fractional difference equations of the form
\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,
where $\mathbb{N}_{1-\gamma}=\{1-\gamma,2-\gamma,3-\gamma,\cdots\}$, $0<\gamma\leq1$, $\Delta^{\gamma}$ 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. |
| first_indexed | 2024-03-10T12:55:37Z |
| format | Article |
| id | doaj.art-e44e3f908d1e4f16859194fc0d8c0a03 |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-03-10T12:55:37Z |
| publishDate | 2023-12-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-e44e3f908d1e4f16859194fc0d8c0a032023-11-21T12:00:13ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362023-12-01148446147910.21136/MB.2022.0157-21MB.2022.0157-21Nonoscillatory solutions of discrete fractional order equations with positive and negative termsJehad AlzabutSaid Rezk GraceA. George Maria SelvamRajendran JanagarajThis paper aims at discussing asymptotic behaviour of nonoscillatory solutions of the forced fractional difference equations of the form \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, where $\mathbb{N}_{1-\gamma}=\{1-\gamma,2-\gamma,3-\gamma,\cdots\}$, $0<\gamma\leq1$, $\Delta^{\gamma}$ 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.http://mb.math.cas.cz/full/148/4/mb148_4_3.pdf fractional difference equation nonoscillatory caputo fractional difference forcing term |
| spellingShingle | Jehad Alzabut Said Rezk Grace A. George Maria Selvam Rajendran Janagaraj Nonoscillatory solutions of discrete fractional order equations with positive and negative terms Mathematica Bohemica fractional difference equation nonoscillatory caputo fractional difference forcing term |
| title | Nonoscillatory solutions of discrete fractional order equations
with positive and negative terms |
| title_full | Nonoscillatory solutions of discrete fractional order equations
with positive and negative terms |
| title_fullStr | Nonoscillatory solutions of discrete fractional order equations
with positive and negative terms |
| title_full_unstemmed | Nonoscillatory solutions of discrete fractional order equations
with positive and negative terms |
| title_short | Nonoscillatory solutions of discrete fractional order equations
with positive and negative terms |
| title_sort | nonoscillatory solutions of discrete fractional order equations with positive and negative terms |
| topic | fractional difference equation nonoscillatory caputo fractional difference forcing term |
| url | http://mb.math.cas.cz/full/148/4/mb148_4_3.pdf |
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