Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions
This study investigates the asymptotic behavior of non-oscillatory solutions to forced-perturbed fractional differential equations with the Caputo fractional derivative. The main aim is to unify the Beta Integral Lemma (Lemma 2) and the Gamma Integral Lemma (Lemma 3) into a single framework. By comb...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/1/6 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588420069720064 |
|---|---|
| author | Said R. Grace Gokula N. Chhatria S. Kaleeswari Yousef Alnafisah Osama Moaaz |
| author_facet | Said R. Grace Gokula N. Chhatria S. Kaleeswari Yousef Alnafisah Osama Moaaz |
| author_sort | Said R. Grace |
| collection | DOAJ |
| description | This study investigates the asymptotic behavior of non-oscillatory solutions to forced-perturbed fractional differential equations with the Caputo fractional derivative. The main aim is to unify the Beta Integral Lemma (Lemma 2) and the Gamma Integral Lemma (Lemma 3) into a single framework. By combining these two powerful tools, we propose new criteria that effectively characterize the asymptotic behavior of non-oscillatory solutions to the given equations. The analysis of such solutions has significant implications in the fields of oscillation and stability theory. Notably, our findings extend prior work by exploring a wider range of equations with more general functions and coefficients, thereby broadening the applicability and deepening the understanding of both asymptotic and oscillatory behaviors. Moreover, the criteria we introduce offer improvements over previous approaches, as demonstrated by the example provided, which highlights the advantages of our results in comparison to earlier methods. |
| format | Article |
| id | doaj-art-72c3f8e5385842d08acd2b5cd8200d1b |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-72c3f8e5385842d08acd2b5cd8200d1b2025-01-24T13:33:20ZengMDPI AGFractal and Fractional2504-31102024-12-0191610.3390/fractalfract9010006Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory SolutionsSaid R. Grace0Gokula N. Chhatria1S. Kaleeswari2Yousef Alnafisah3Osama Moaaz4Faculty of Engineering, Cairo University, Orman, Giza 12221, EgyptDepartment of Mathematics, Sambalpur University, Sambalpur 768019, IndiaDepartment of Mathematics, Nallamuthu Gounder Mahalingam College, Coimbatore 642001, IndiaDepartment of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi ArabiaThis study investigates the asymptotic behavior of non-oscillatory solutions to forced-perturbed fractional differential equations with the Caputo fractional derivative. The main aim is to unify the Beta Integral Lemma (Lemma 2) and the Gamma Integral Lemma (Lemma 3) into a single framework. By combining these two powerful tools, we propose new criteria that effectively characterize the asymptotic behavior of non-oscillatory solutions to the given equations. The analysis of such solutions has significant implications in the fields of oscillation and stability theory. Notably, our findings extend prior work by exploring a wider range of equations with more general functions and coefficients, thereby broadening the applicability and deepening the understanding of both asymptotic and oscillatory behaviors. Moreover, the criteria we introduce offer improvements over previous approaches, as demonstrated by the example provided, which highlights the advantages of our results in comparison to earlier methods.https://www.mdpi.com/2504-3110/9/1/6differential equationfractionalhigher ordernon-oscillation |
| spellingShingle | Said R. Grace Gokula N. Chhatria S. Kaleeswari Yousef Alnafisah Osama Moaaz Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions Fractal and Fractional differential equation fractional higher order non-oscillation |
| title | Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions |
| title_full | Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions |
| title_fullStr | Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions |
| title_full_unstemmed | Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions |
| title_short | Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions |
| title_sort | forced perturbed fractional differential equations of higher order asymptotic properties of non oscillatory solutions |
| topic | differential equation fractional higher order non-oscillation |
| url | https://www.mdpi.com/2504-3110/9/1/6 |
| work_keys_str_mv | AT saidrgrace forcedperturbedfractionaldifferentialequationsofhigherorderasymptoticpropertiesofnonoscillatorysolutions AT gokulanchhatria forcedperturbedfractionaldifferentialequationsofhigherorderasymptoticpropertiesofnonoscillatorysolutions AT skaleeswari forcedperturbedfractionaldifferentialequationsofhigherorderasymptoticpropertiesofnonoscillatorysolutions AT yousefalnafisah forcedperturbedfractionaldifferentialequationsofhigherorderasymptoticpropertiesofnonoscillatorysolutions AT osamamoaaz forcedperturbedfractionaldifferentialequationsofhigherorderasymptoticpropertiesofnonoscillatorysolutions |