Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms
In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The result...
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MDPI AG
2020-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/6/1037 |
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| author | Jehad Alzabut James Viji Velu Muthulakshmi Weerawat Sudsutad |
| author_facet | Jehad Alzabut James Viji Velu Muthulakshmi Weerawat Sudsutad |
| author_sort | Jehad Alzabut |
| collection | DOAJ |
| description | In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior. |
| first_indexed | 2024-03-10T18:54:35Z |
| format | Article |
| id | doaj.art-b44cba2775994f6c8b5f2c6ed157aa47 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:54:35Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b44cba2775994f6c8b5f2c6ed157aa472023-11-20T04:54:22ZengMDPI AGMathematics2227-73902020-06-0186103710.3390/math8061037Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping TermsJehad Alzabut0James Viji1Velu Muthulakshmi2Weerawat Sudsutad3Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, Periyar University, Salem 636 011, Tamilnadu, IndiaDepartment of Mathematics, Periyar University, Salem 636 011, Tamilnadu, IndiaDepartment of General Education, Navamindradhiraj University, Bangkok 10300, ThailandIn this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior.https://www.mdpi.com/2227-7390/8/6/1037generalized proportional fractional operatoroscillation criterianonoscillatory behaviordamping and forcing terms |
| spellingShingle | Jehad Alzabut James Viji Velu Muthulakshmi Weerawat Sudsutad Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms Mathematics generalized proportional fractional operator oscillation criteria nonoscillatory behavior damping and forcing terms |
| title | Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms |
| title_full | Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms |
| title_fullStr | Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms |
| title_full_unstemmed | Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms |
| title_short | Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms |
| title_sort | oscillatory behavior of a type of generalized proportional fractional differential equations with forcing and damping terms |
| topic | generalized proportional fractional operator oscillation criteria nonoscillatory behavior damping and forcing terms |
| url | https://www.mdpi.com/2227-7390/8/6/1037 |
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