Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions
This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/4/325 |
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| author | Jehad Alzabut Said R. Grace Jagan Mohan Jonnalagadda Shyam Sundar Santra Bahaaeldin Abdalla |
| author_facet | Jehad Alzabut Said R. Grace Jagan Mohan Jonnalagadda Shyam Sundar Santra Bahaaeldin Abdalla |
| author_sort | Jehad Alzabut |
| collection | DOAJ |
| description | This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish the main results, an analogous representation for the main equation, called a Volterra-type summation equation, is constructed. Two numerical examples are provided to demonstrate the validity of the theoretical findings; no earlier publications have been able to comment on their solutions’ non-oscillatory behavior. |
| first_indexed | 2024-03-11T05:15:15Z |
| format | Article |
| id | doaj.art-9fda8e0668a04b83981f7c68268cea30 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T05:15:15Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-9fda8e0668a04b83981f7c68268cea302023-11-17T18:18:50ZengMDPI AGAxioms2075-16802023-03-0112432510.3390/axioms12040325Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory SolutionsJehad Alzabut0Said R. Grace1Jagan Mohan Jonnalagadda2Shyam Sundar Santra3Bahaaeldin Abdalla4Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaTurkey Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Giza 12221, EgyptDepartment of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad 500078, Telangana, IndiaDepartment of Mathematics, JIS College of Engineering, Kalyani 741235, West Bengal, IndiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaThis work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish the main results, an analogous representation for the main equation, called a Volterra-type summation equation, is constructed. Two numerical examples are provided to demonstrate the validity of the theoretical findings; no earlier publications have been able to comment on their solutions’ non-oscillatory behavior.https://www.mdpi.com/2075-1680/12/4/325non-oscillatory solutionsasymptotic behaviorcaputo nabla fractional differencenabla fractional difference equations |
| spellingShingle | Jehad Alzabut Said R. Grace Jagan Mohan Jonnalagadda Shyam Sundar Santra Bahaaeldin Abdalla Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions Axioms non-oscillatory solutions asymptotic behavior caputo nabla fractional difference nabla fractional difference equations |
| title | Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions |
| title_full | Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions |
| title_fullStr | Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions |
| title_full_unstemmed | Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions |
| title_short | Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions |
| title_sort | higher order nabla difference equations of arbitrary order with forcing positive and negative terms non oscillatory solutions |
| topic | non-oscillatory solutions asymptotic behavior caputo nabla fractional difference nabla fractional difference equations |
| url | https://www.mdpi.com/2075-1680/12/4/325 |
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