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The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations
Open AccessArticle

Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms

by Jehad Alzabut 1,*,†, James Viji 2,†, Velu Muthulakshmi 2,† and Weerawat Sudsutad 3,†
1
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2
Department of Mathematics, Periyar University, Salem 636 011, Tamilnadu, India
3
Department of General Education, Navamindradhiraj University, Bangkok 10300, Thailand
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(6), 1037; https://doi.org/10.3390/math8061037
Received: 29 May 2020 / Revised: 22 June 2020 / Accepted: 23 June 2020 / Published: 25 June 2020
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. View Full-Text
Keywords: generalized proportional fractional operator; oscillation criteria; nonoscillatory behavior; damping and forcing terms generalized proportional fractional operator; oscillation criteria; nonoscillatory behavior; damping and forcing terms
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Alzabut, J.; Viji, J.; Muthulakshmi, V.; Sudsutad, W. Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms. Mathematics 2020, 8, 1037.

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